To better answer your question, a video would be very helpful.
Because you're description is so vague, it's difficult to tell how he's handling the jumping. There are many factors to take into consideration here.
1. Is he in the right condition? Most horses peak out at a specified height not because physically they cannot go higher, but simply because their lack of conditioning doesn't allow them to do so.
2. Training. What heights have you been jumping now? Is he comfortable at these heights? Are you allowing him to be complacent? Are you asking him to jump properly from correct distances? Gymnastics would be a very good idea to begin with.
3. How is his flatwork? If he is lazy as you say over fences then you need to go back to flatwork and condition him & ask him to use the muscles he'll be needing over fences. This ties in with the conditioning.
I could really go on, but those I feel are the main points. It sounds to me like this horse needs a lot of conditioning and gymnastic work before even thinking about moving up or competing at the higher jumps.
Just my opinion anyway.