In Buddhism, bad Kamma begins with a bad intention. What can we say about animals, let's say a tiger or a lion that kills other living beings by instinct? They don't have the same understanding as we do as human beings and they simply cannot become vegetarians: so are they creating bad Kamma that might ripen in a next life? For instance, if I used to be a lion will I suffer bad Kamma consequences in this human life because I killed and ate living beings?
Bad Karma are caused by the three evil roots.
Doing something bad without knowing it is bad falls under ignorance. Ignorance is there in all bad Karmas. But in the case of a lion killing a deer, it is stronger compared to a human killing a deer, given that he knows it is wrong. So the lion has strong ignorance on top of strong aversion and craving. That makes the Karma worse. One thing you have to understand about the law of Karma is that it is a law of the nature. It is not a god. So there's never a question of whether it is fair or not. Is it fair for children to get burnt if they touch fire without knowing it burns? Probably not! But the fire doesn't have a conscious to decide whom to burn or not to burn.
Within Karma it is the intention or volition behind the action that is important not the action itself. So if we assume that an animal (lion etc..) acts primarily out of instinct then I would say that animals don't have volition (they can't help it) therefore they don't generate bad Karma. However they don't generate good Karma either so they are stuck. The previously accumulated bad Karma will eventually fizzle out be that might take a while, a long long while.
This leads directly to the notion of the preciousness of human life in the four reminders. Once you are in a lower realm then it is hard to get out so birth as a human (the only place where enlightenment is possible) is very very rare. If OP has been lucky enough to be born as a human then make the best of if. It might not happen again for a long while.
It's also worth noting that in the Tibetan wheel of life there is the notion of other power. In each realm, including the animal one, there is a Buddha figure as shown above. The figure is there to do whatever they can to assist the beings (animals) to get out of their situation. Sometimes it;'s just so hard to do it yourself that another power is required. This answer to another post gives some good further detail on that point.
When a lion sets out to kill a pay, 1) it knows it is a living creature, 2) it has the intention to eat (kill) it, 3) it chases after to kill it (method) and 4) finally catches it and kills it. So the Karma regarding killing is complete and would give results.
When you get a animal life you are forced to do bad Karma thus you are trapped in the lower realms for an extremely long time. Also there is always agitation (in fear, lack of food, killing for food) so the metal state generated are most of the time very bad.
Further see my answer to: Do the same rules of Karma apply to animals?
By the logic of bad kamma, no animal will evolve into human. How do humans become humans then?
Whenever we are eating a fruit and a vegetable we are killing millions of cells which are alive. When we are breathing we are killing countless viruses, parasites etc. We are constantly gathering bad kamma. But breathing and eating are automatic functions. We are not responsible for it. So how can we be responsible for bad kamma then?
Intention come from mind and animals do not have mind. Only humans do. There is no question of bad kamma when instincts are involved. In-fact even sex if it is driven through instincts has no karmic effect. When it is mind induced which is the case 99% time it has karmic effects. Modern men and women do not have natural sex any more.
In case of animals evolution is automatic. They are unconscious beings. They do not accumulate bad kamma otherwise evolution will stop. But once an animal graduates into human then there is no automatic evolution. Humans need to put conscious efforts to become perfect. Nature will not help. Only through right understanding and right efforts humans progress further.