This answer is interpretive and contains a speculative analysis about Lennie and his motivations.
Lennie does not kill little animals accidentally. He tells George that he usually kills them because they struggle to get away and sometimes bite him. Lennie is looking forward to tending rabbits for two reasons. One is that he will have the pleasure of petting soft little animals. The other reason is that, since he is the one who tends the rabbits, he will be the one who kills them when they are fat enough to eat. In other words, he gets pleasure from petting little animals, and he also gets pleasure from killing them. This pleasure he derives from petting and killing animals is symptomatic of a violence which Lennie does not understand and which George does not suspect until he sees the dead body of Curley's young wife in the barn. George
...was down on his knees beside her. He put his hand over her heart. And finally, when he stood up, slowly and stiffly, his face was as hard and tight as wood, and his eyes were hard.
George is beginning to feel guilty of the girl's death because he brought Lennie to this ranch, because he protected him from the mob in Weed, and because he "should have knew" that Lennie was becoming dangerous. Lennie can't be blamed for being what he is, but that doesn't change what he has become.
"I should of knew," George said hopelessly. "I guess maybe way back in my head I did."
That is the most significant passage in the book. George "should have knew" that Lennie's violence couldn't be controlled. Perhaps Lennie was not interested in feeling the girl's soft dress, but he was sexually attracted to the girl herself. When she got the idea that he was trying to rape her, it might be she wasn't far from the truth--although Lennie himself probably didn't understand his own urges. George assumes that something similar happened with Curley's wife in the barn. Lennie didn't know what he was doing. Lennie is becoming a monster because he can't control his desires and his enormous physical strength.