Any answer received regarding John Steinbeck's character choice in Of Mice and Men will be an assumptive one (given readers can only assume why Lennie is as he is).
Therefore, based upon my own personal interpretation of the text, I believe that Lennie was created as a character, for the novel, based upon the fact that one of the main themes of the novel is about friendship.
Relationships of characters, many times, mirror ones typical of real life. In real life, many friendships are made between people who benefit each other in different ways. In the novel, Steinbeck is holding true to typical friendships.
In the novel, both Lennie and George benefit by the relationship. Both men need each other in order to live. Even when George kills Lennie, he is doing so in order to look out for Lennie.
Another reason why Steinbeck may have chosen Lennie's character is the fact that readers are needed to engage with him and have sympathy for him. This sympathy and engagement creates a bond between the reader and the story. Without this type of relationship, the reader will fail to see underlying meaning in the text itself.
John Steinbeck intended to adapt his novella into a play to be produced in New York. This is discussed in eNotes Study Guide "Introduction." The novella itself is unusual in that it is limited to only two sets and almost all the exposition is conveyed through dialogue. This obviously made it easy to convert the book into a play. One reason Steinbeck made one of the two main characters feeble-minded must have been that George would have to explain everything to him--and in doing so he would be conveying necessary information to the audience.
Just to take one example, Lennie keeps asking George to tell him about their plan for the future. This is essential to the story and to the idea that the best laid plans of mice and men are often disappointed. George patiently explains that they are going to save their money, buy a little farm, and become independent.
No doubt Steinbeck had other reasons for creating the character of a mentally handicapped Lennie, but what I have suggested may have been the primary reason. Steinbeck may have been mainly concerned about getting his story on the stage in New York, because that was, and still is, the intellectual and cultural capital of the United States, whereas California in the 1930's had a small population and was mainly an agricultural state.
Steinbeck intended to have George kill Lennie in the final chapter, so in the opening chapter he has George instruct Lennie to come back to their present campsite by the river and hide until George can reach him. Having a feeble-minded character made it easy for Steinbeck to convey exposition in the form of dialogue. This in turn made it easy to convert the book to a stage play.