What are some quotes from the novel Of Mice and Men that show Lennie's dependance on George?
You might want to focus on the opening chapter and consider how the characters are presented and what that says about their relationship. From the very start, it is clear that George is in a position of power over Lennie, and as the story develops, we discover more precisely of what that position of power entails and about their relationship. Consider, for example, how George is described as leading the way into the clearing, with Lennie walking behind. It is clear that George is the leader.
Then think of what George says to Lennie when Lennie starts drinking water from the pool:
"Lennie!" he said sharply. "Lennie, for God's sakes don't drink so much." Lennie continued to snort into the pool. The small man leaned over and shook him by the shoulder. "Lennie. You gonna be sick like you was last night."
Note the way that Lennie is presented here, as we see him "snorting into the water like a horse." He is clearly unable to know what is good and what is not good for him, and lacks both restraint and sense. It is George's job to look after him and to make sure he doesn't hurt himself, like he has already done from drinking too much the night before. George is clearly the carer of Lennie, because Lennie is not able to look after himself.
Nearly every conversation George and Lennie have displays some element of Lennie's dependence on George. Through direct characterization, we learn early on that George made a promise to look out for Lennie when Lennie's Aunt Clara died. As a fulfillment of that promise, George explains in a conversation with Slim that he has had to constantly move from one place to another because of the foolish and naive mistakes Lennie has made. We learn that it was George's quick-thinking that saved both their lives after Lennie unwittingly tore a girl's dress at their previous place of employment. When a lynch-mob came after them, assuming that Lennie had been attempting to rape the girl rather than just feel the soft material of her dress, George formulated an escape that brought them to the setting of the novel as we are reading it.
Perhaps Steinbeck's best depiction of Lennie's dependence on George comes from the scene where all of the ranch hands have gone into town and Lennie is left to wander around the ranch alone. He finds himself in Crooks' room, drawn in like a moth to his light. Out of his own frustration with the cruel and lonely hand that has been dealt to him, Crooks engages Lennie in a conversation where he hypothesizes about what would happen to Lennie if "George don't come back no mo'." He tells Lennie that he is "crazy as a wedge" and would be locked up in a "booby hatch" if left on his own. Lennie, who is not able to comprehend a hypothetical situation becomes, at first, agitated and then angry with Crooks for even suggesting George might not return, thinking that he intends to hurt George. His very reaction supports the idea that he would not be able to function in normal society on his own without George as his caretaker.