In situations involving lies and/or violence, does Buddhism teach siding with truth and peace against lies and violence, or does it teach ethical neutrality i.e. not taking stance on such subjects?
IMO, your question dances around the delicate subject of "Should Buddhists go to war in defence of the side that is innocent?" Should Buddhists fight aggressors? The answer isn't simple, because what constitutes "a Buddhist" isn't simple. Which "Buddhist" do we mean when we ask this question? Do we mean the members of the Bhikṣusaṃgha? Do we mean "the four communities" of laypeople and mendicants? Do we mean just anyone who is "into" the Buddha and the Dharma?
Buddhism has difficult advice to-do with dealing with war, with conflict. When Virūḍhakarāja massacred the Śākyas of Kapilavastu, the Buddha watched passively from the top of a hill while shaded by the canopy of a sparse tree. He didn't rush down with his hand held out in the "stopping mudrā" in the manner that it is said that he supposedly stopped the elephant. While Russia attacks Ukrainians, the Buddha unfortunately would have likely sat at the top of the hill, shaded by a tree, and watched. That's a difficult look. It certainly seems "ethically neutral."
Yet, we know that Buddhism, that the Buddhadharma, is not actually "ethically neutral." Karma itself is predicated upon morality and ethics.
No Buddhist textual tradition records the thoughts of the Buddha while he watched the Śākyas of Kapilavastu, the members of his own family, die. Buddhist tradition passes down several accounts that give various hagiographical details, such as that those Śākyas were Arhats, and that they refused to fight, not taking up their weapons, meeting death gracefully. I read that hagiography in a Pāli source, but am having difficult finding it again at the moment. In the meantime, I also found this version of the events, which somewhat corresponds to the mythohistory that I had read previously...
Everyone was killed except those who entered the battlefield and symbolically rejected violence by holding blades of grass or reeds between their teeth. Everyone was killed: man, woman, child. The Buddha did not stop the slaughter.
While returning home, Vidudabha and his soldiers slept on a dry riverbed. Ants came at night and carried those who were sinless to the riverbank. The rest, including Vidudabha, were drowned in a flash flood, and their bodies were swept away by the raging river into the sea.
(Devdutt Pattanaik summarizes)
I know a version of this which has the incredible (and rather unbelievable) detail that all of the Śākyas rejected violence, that all of them were holy, and that all of them achieved liberation. Either way we tell the story, the Buddha watched from either the top of a hill or from under a tree outside the city boundaries.
If the Ukraine had been invaded during the Buddha's time, if the aggressing troops had been much more bloodthirsty than contemporary Russian soldiers, if there was a genocide, if the Buddha had been born there, would Buddhists today be saying that all of the Ukrainians of Kiev were Arhats and that all of them died holy and noble?
It's a very impressive hagiography, but it does little to help the theorized massacred Ukrainians of the past in this thought experiment.
Modern democracies are unlike the kingdoms of the Buddha's time as much as they are like them. Democracies are states, just like those kingdoms, but "kinghood" is participatory through the institutions of the democracy. When King Louis XIV was arrested by revolutionary soldiers in the name of the French State, he said, "L'État, c'est moi," or "The State? That's me." The king is the state, is the body politic, in such a system of governance. In a democracy, the body politic is diluted through several offices and institutions. When persons have a say in their country's politics, they become part of that body politic. When the ministers obey the will of the people, both the ministers and the people are the body politic.
When the Buddha speaks of kings and their ministers, he does not universally condemn them per se, even though talk of kings and ministers, etc., is talk of "lowly topics" (Sāmaññaphalasutta, DN 2, as translated by Venerable Ṭhānissaro). Concerning armies, he says that:
"When a warrior strives & exerts himself in battle, his mind is already seized, debased, & misdirected by the thought: 'May these beings be struck down or slaughtered or annihilated or destroyed. May they not exist.' If others then strike him down & slay him while he is thus striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the hell called the realm of those slain in battle. But if he holds such a view as this: 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle,' that is his wrong view. Now, there are two destinations for a person with wrong view, I tell you: either hell or the animal womb."
(Yodhājīvasutta SN 42.3 translated by Ven Ṭhānissaro)
This reads like a blanket condemnation of all soldiers, but is technically a condemnation of the "warlike mindset." Maybe it's a difference without distinction.
Kings are worldlings, worldlings entangled in the world, entangled in the geopolitics they were born into. These were, after all, hereditary monarchies. When an aggressor attacks a dominion under the care of a king, the Buddha says:
Here, bhikkhu, a wheel-turning monarch, a righteous king who rules by the Dhamma, relying just on the Dhamma, honoring, respecting, and venerating the Dhamma, taking the Dhamma as his standard, banner, and authority, provides righteous protection, shelter, and guard for the people in his court. Again, a wheel-turning monarch, a righteous king who rules by the Dhamma, relying just on the Dhamma, honoring, respecting, and venerating the Dhamma, taking the Dhamma as his standard, banner, and authority, provides righteous protection, shelter, and guard for his khattiya vassals, his army, brahmins and householders, the people of town and countryside, ascetics and brahmins, and the animals and birds. Having provided such righteous protection, shelter, and guard for all these beings, that wheel-turning monarch, a righteous king who rules by the Dhamma, turns the wheel solely through the Dhamma, a wheel that cannot be turned back by any hostile human being.
(Cakkavattisutta AN 3.14 translated by Venerable Bodhi)
Having provided righteous protection, the Cakravartin "turns the wheel" via the Dharma. There is a sequence of events there. Having provided the protection, having established the prosperity, the Wheel-Turner then rules by the Dharma and "turns the wheel." Compare:
in the royal capital of Ketumati a king named Saṅkha will arise, a wheel-turning monarch, a just and principled king. His dominion will extend to all four sides, he will achieve stability in the country, and possess the seven treasures. He will have the following seven treasures: the wheel, the elephant, the horse, the jewel, the woman, the treasurer, and the counselor as the seventh treasure. He will have over a thousand sons who are valiant and heroic, crushing the armies of his enemies. After conquering this land girt by sea, he will reign by principle, without rod or sword.
(Cakkavattisutta DN 26 translated by Venerable Sujāto)
After he conquers, the Wheel-Turner forsakes the rod and the sword. This one is a little more difficult, because it is about conquering, not about defending (like the other one was). I will point out, however, that what was conquered in this version of the Cakkavattisutta was "the armies of his enemies," implying, to me, that this is a situation of traditional perpetual warfare over territory. The Wheel-Turner needn't be an Alexander-like figure who conquers for the sake of conquest. Perhaps that is an unjustified reading on my part, softening this difficult passage by asserting that a Wheel-Turner would not strike an unprovoked blow against a neighbouring "non-enemy." Maybe that's naïve.
Either way, as in the previous example, the Wheel-Turning King must establish a peace before he can establish a Dharma.
This, IMO, is the closest the Buddha comes in the Pāli Canon (I've not yet read the Humane Kings Sūtra, but I have it on good faith that it also addresses these matters similarly) to a direct answer to the OP. In a democratic society, where "kinghood" is diluted, the widely-distributed composite body politic must work to establish peace and to diminish chaos and warfare. After that, focus can be re-aligned to "establishing the Dharma," such as the teachings of renunciation and inaction that are so fraught in times of war. The inaction of Gautama Buddha, who renounced the world and did not re-entangle himself in the world for the sake of saving the Kapilavastu Śākyas, is difficult if we look to the Buddha here as our direct guide. Certainly, an Arhat practicing for individual liberation might not take any measures at all to right wrongs. "Such is saṃsāra," we might imagine them dispassionately saying.
The path of world-renunciation is not the path of politics. The path that transcends the world is not the path of the world. The Buddha could not be both a Cakravartin Dharmarāja and a Samyaksaṃbuddha, despite the Brahmanical prophecy of the 32 marks being shared between the two.
In times of war, worldlings must defend themselves for the sake of the peace that makes practice possible. Certainly, it's not impossible to practice Buddhism in a country under attack, but it is not "ideal conditions" either. To suggest that all non-Buddhas must abstain from all violence is impractical and foolhardy advice. It is expecting all of the people of the world to be saints and sages, like the supposed saints and sages of Kapilavastu who met their death willingly. It is not humane to expect this conduct of persons who are not saints and sages and who are simply ordinary persons. It is extraordinary conduct, and to expect it of the ordinary is foolish. The ordinary man is not wicked, but he isn't a saint either. Them not being wicked but also not being saints, it would not be reasonable or humane to suggest that the Ukrainians adopt behaviours based on the precedence of the mythology surrounding the fall of Kapilavastu. The Ukrainians are not collectively saints and sages. They are ordinary human beings. We oughtn't expect them to act like sages from a medieval Indian story. That's an example of getting one's wires crossed, if you're expecting a population of ordinary people to just lay down and let themselves be trampled.