You need to speak to your doctor about this. Personally i would avoid the Barra schools..
They are too focused on winning trophies and slap happy with the belts which i am completely against as it does not teach real self defense. It teaches sport. Gracie Jiu Jitsu is a good style to learn but i avoid the Barra trained students. In fact i re-grade any Barra trained students that come to train with me because i do not agree with the standard they teach.
You should baby the leg and do Jiu Jitsu once a week or once a month and do weight training to strength the thing around the lap band my back is all messed up but I still do weights it helps make everything therapy for messed up ligaments.
My immediate reaction would be no, that there could be complications, but only a doctor could tell you for sure.
I really want to learn self-defense so I can know how to defend myself and to get exercise. I had lap band surgery in 2009 and although I only had one fill since I didn't like the experience (long story and not the point of this question) I haven't lost much and regained some. I want to focus on improving my eating habits and get good exercise. I've been thinking of getting into Brazilian Jiu Jitsu ever since I heard it was one of the best forms of self-defense. I talked to a guy at a local Gracie Barra school on the phone for awhile earlier but forgot to ask him. I won't see my Primary Care Physician until two weeks from now, so I figured it wouldn't hurt to get opinions here. :)