With no data to back it up, and just going off what I watched for 7 years, my guess would be the left side, although I doubt there is a huge difference.
From 16-24 ft on the left side (but not in the corner), he is shooting 44.0%. But on the right side he's shooting 33.3%.
From beyond the 3pt arc on the left side (but not in the corner), he is shooting 40.2%. On the right side he's shooting 30.7%.
Which is something I stress, and was kind of brought up with Kyrie the other day, LeBron knows where he is more effective at on the floor and that is where he takes a higher percentage of his shot attempts. Can't say that for many NBA players. They all aren't that smart. Though it's not as easy as it sounds.
I don't think LeBron goes to the left because he's more comfortable shooting from that side. I think it's just more likely for him to succeed from that side since he's overplayed to the right. But you're right, he knows this, he takes what the defense gives him.