What is meant by "claims the bull’s place, roars his lion’s roar in the assemblies" and was an actual loud lion-like sound ever uttered by the Buddha? One example of the quote is mentioned in https://suttacentral.net/mn12/en/sujato
The Pali word that's translated "lion's roar" is sīhanāda.
This dictionary lists a few Pali suttas where it's found, and gives a definition as,
sīhanāda : (m.) lion's roar; a brave speech.
I think's it meant to imply unafraid or confident, and not just loud.
Google suggests it's used in Tibetan teaching too, in a phrase or doctrine related to fearlessness -- for example here:
In the third turning of the wheel of dharma, the Buddha speaks of the lion's roar. The lion's roar is the fearless proclamation that anything that happens in our state of mind, including emotions, is manure. Whatever comes up is a workable situation; it is a reminder of practice, and it acts as a speedometer. It is a way to proceed further into the practice of meditation.
In this way we begin to realize that all kinds of chaotic situations that might occur in life are opportune situations. They are workable situations that we mustn't reject, and mustn't regard as purely a regression or going back to confusion at all. Instead, we must develop some kind of respect for those situations that happen in our state of mind.
But I don't know how to find a reference for that (third turning).
If or given that it is associated with the "third turning" I note that it's also associated with the first -- i.e. the Pali suttas -- in that the title of DN 26 is sometimes given as
The Wheel-Turning Monarch
... and sometimes as ...
The Discourse on the Lion-roar of the Wheel-turner
Cakkavatti Sihanada Sutta
... of which this analysis by Piya Tan includes a page-long definition. Here's a quote from that but you might want to read the whole definition by following the link.
Based on all this, the commentaries say that a lion-roar is a roar of fearlessness (abhīta,nāda, DA 3:827), a fearless response, rejoicing in another’s remark or one’s own (DA 3:844), a statement of supremacy (or a foremost remark), of fearlessness, which cannot be debunked (seṭṭha,nādaṁ abhīta,nādaṁ appaṭi,nādaṁ, AA 2:303, 4:171), such as declaring the presence of recluses (samaṇa) in the teaching (MA 2:7). There are at least a couple of discourses that are themed on the “lion-roar,” that is, the (Anicca) Sīha Sutta (S 22.78), the (Catukka) Sīha Sutta (A 3.33) and the (Dasaka) Sīha Sutta (A 10.21).