It is easy to see Lenny as an innocent who had simple longings, an unfortunate due to his disability but fundamentally a sympathetic character; however, it seems to me that while most of his violence was accidental and he did not start the fight with Curly that resulted in Curly's hand being injured, there is evidence that he is not completely incapable of initiating violence and is in no way generous or interested in the welfare of others, including -- and especially -- George.
When Crooks, the injured ranch hand (also disabled,also excluded), teases Lenny (foolishly and somewhat sadistically but perhaps more cruelly than he had intended or, perhaps deliberate in his cruelty) about George not returning, Lenny rapidly becomes angry and it seems very possible that he might have attacked and injured Crooks. Even in his fight with Curly, although clearly not Lenny's fault, he might well have killed Curly had no one intervened.
But again, where in the novel does Lenny express any interest in George beyond the place he hopes they live in together? Every single conversation with George centers around Lenny: what Lenny wants or what Lenny is doing wrong that might endanger himself or them both.
Even his desire to handle animals is fundamentally selfish.
I wonder if this was deliberate on Steinbeck's part, to have a character who despite his innocence is not actually particularly kind or generous.
EDIT: To show that I am not a very sophisticated reader, I am rewatching the Hangover, Part II in which we see the nasty side further of Alan; Alan reminds me of Lenny.