This is a tough one, but as a mom/grandmom and retired teachers, I have a few thoughts. One is that over all of my years with kids, I have let go of the idea that kids are ever "lazy" about school. When kids are anxious, and fear failure, just getting started on school work is a HUGE problem. When they are depressed, the work and all that effort feels pointless, so they go through the motions. I'd suggest helping him, but not by pressuring him to "get it done". I'd sit with him and help him to prioritize one small task and then help him to plan out and organize that task. When he's done, tell him to let you know. Then let him reward himself with a game, a snack, a nap, whatever. Encourage him to do another task. Be concrete.

It's a lot easier to envision "Complete these ten math problems" than "do this entire pile of work that is overwhelming me."

I'd also suggest a tutor to help him get it done. Good luck!

Most of all, remember that he is not his brother; comparing them isn't fair or helpful.