What are three reasons why George and Lennie have a true friendship in Of Mice and Men?

Assuming that you are asking for evidence showing that George and Lennie's friendship is "true", here are three determining factors. 

1) George is loyal to Lennie

Regardless of how angry George gets with Lennie, or how much heat he gives him everyday, George is determined to keep Lennie by his side until the end. Notice that George has spend his entire life next to Lennie. While the men knew one another since childhood, the only solid evidence in the story that shows a reason why George decided to become Lennie's keeper is that the latter's aunt died, and George decided to take care of him. 

I knowed his Aunt Clara. She took him when he was a baby and raised him up. When his Aunt Clara died, Lennie just come along with me out workin'.Got kinda used to each other after a little while."

This is a demonstration of true loyalty. Sure, George has his days when he even acknowledges being mean to Lennie. However, he always calms down and, even when he kills Lennie out of mercy, he is clear in telling him that he is not mad at him. 

2) Their friendship has withstood obstacles

George has every excuse to run away from Lennie. What can Lennie do? Chase after him? Hardly. Tell his aunt? Impossible. Therefore, what has stopped George from running away every time he and Lennie get into trouble? We know that the two men have had issues with the law before. Most of these issues are caused by Lennie, whose size and body strength are inversely proportional to his cognitive skills.

Therefore, Lennie often ends up doing things that are as inappropriate as they are downright wrong. In the town of Weed, for example, he touched a girl's dress in a way that made the girl think that he was going to rape her. Lennie has also been known by George to accidentally kill animals and other things, inadvertently. Still, fights and all, the two have remained together and did stay together until Lennie's death. 

3. They have made plans for the future

The previous two examples show evidence from the past and the present. Lennie and George have come a long way since childhood and, at the start of the novel, continue to be together against all odds. One more evidence about the true nature of their friendship is the fact that they plan together.

Their plan, which eventually is shared with Candy and Crooks, is to "live off the fat of the land", that is, to get a farm, tend to it, and reap its benefits. They do keep this dream alive throughout the novel, and right until Lennie's death. The American Dream is shared by these two men, and they do not falter; they continue to dream and, in this dream, they also remain together. 

Therefore, the true nature of the friendship of Lennie and George is based on the fact that they share a history and plan to establish a future together as well. They find strength in their unity, and they will continue to stay together until they can no longer be.