If we define Lennie’s ignorance broadly, we might be able to identify several examples of places where he is fearful due to a lack of knowledge, wisdom or awareness in the moment.
First, Lennie’s insecurity in his relationship with George seems to be unfounded. He is “ignorant” of the depth of the bond that George feels for him. This causes Lennie to be afraid of George’s anger to exaggerated degree. (He shouldn't be afraid that George will be permanently upset over a complaint about ketchup, for instance.)
While the two men are at the river at the beginning of the novel, Lennie threatens to go off in the hills and "live by myself." This behavior from Lennie seems to be due to the fact that Lennie is either willfully ignorant of George’s feelings of friendship and responsibility or because he is trying to manipulate George. It's probably both.
While Lennie has some the capacity to wheedle, it seems that he is most likely actually afraid that George will leave him one day. And as much as we might see him playing on George’s emotions as a way to get what he wants, Lennie is almost certainly also acting out of fear of being left on his own. Yes, he wants to keep his mouse, but more than that, he craves human connection and the safety of his friendship with George. So, it’s ironic that he threatens to go off and live in the hills alone.
Second, Lennie seems to be worried about the new ranch that he and George are going to. This is partly because he had a bad experience at the last ranch in Weed, but it is also partly due to a simple fear of the unknown. This is a very plain example of a fear born out of ignorance.
Third, and perhaps the most pointed example in the novel of Lennie being fearful due to ignorance, is when he panics and kills Curley’s wife.
In this scene, Lennie kills Curley’s wife because he just cannot think of any other way to quiet her. His fear of being caught with her takes over. If Lennie were to have more knowledge and more consciousness in this scene, he would not panic. But his social ignorance quickly becomes translated into a moral and legal ignorance. He kills a woman to avoid being caught talking to her because he is afraid of the consequences of that lesser, far more forgivable act.
Lennie is ignorant of his actions in the sense that he doesn’t seem to know he is killing her. And he is ignorant also in the sense that he seems to have no alternative ideas as to what he should do in this situation. He fears being caught with Curley’s wife more than he fears committing (and being caught for) murder.
Generally speaking, Lennie is able to be manipulated by others like George because they can make him afraid.
Lennie is afraid that he will not be allowed to tend rabbits on a farm that he does not yet own, for instance. This fear is linked to his innocence which is, of course, part of his ignorance too. It’s a fear that is used as a way to get Lennie to “stay in line” but it is certainly evidence of a through-line between Lennie's ignorance and his fear.
Some of his ignorance may be noble if we see his belief in the possibility of land ownership as a noble dream. This is the same "ignorance" that George and Candy allow themselves to engage in. But this nobility does not raise any of these men above the moral and economic fray that has characterized their adult lives to this point. It links them instead to a stubborn insistence on a right to dream and a right to believe in their dreams.
But, in Lennie's case, this belief comes at a cost. His investment in the reality of the dream is, arguably, an "ignorant" investment. And this is exactly what he fears to lose when Curley's wife starts screaming in the barn.