The question, "In John Steinbeck's novel Of Mice and Men, do George and Lennie have a healthy relationship?," is a subjective one. What this means is that different readers will feel differently about the relationship between George and Lennie. Answers, therefore, will vary between readers and their interpretations and views on the relationship in question.
That being said, all relationships have a little bit of "unhealthiness" to them (at one point or another). There are times where only one person gives and one person receives. There are other times where one person is always, and will always, be required to look out for the other person. I think the only way to really examine the healthiness of their relationship is to look at the meaningful conversations between the men.
In chapter one, after the men fight about ketchup and Lennie threatens to run away, George apologizes to Lennie and tells him that he does not want him to leave.
No-look ! I was jus' foolin', Lennie. 'Cause I want you to stay with me.
Here, George could have agreed to let Lennie run off and would not have had to been worried about him ever again. Instead, he (George) realizes that they do have a special relationship.
One thing that must be said though is that relationships are healthy to different people for different reasons. Lennie needs George to take care of him. George needs Lennie to feel good about the promise he made to Aunt Clara. In the end, both men need each other. One could say that this justifies a healthy relationship.