He is a 15 year old Thoroughbred and he may be jumping the fence because he LIKES to and has learned how and that he can. There are horses like that.
At 15 maybe you would be better off simply NOT free lunging him at all considering the tibia with screws in it. Just ride him. If the Mini is along and it is no issue, then ride him with the mini along and don't make it an issue.
Quite honestly, there are times when you must pick your battles. If the situation is not a problem, don't make it a problem (the mini along business). If at some point you get another horse, the thing to do would be to not let this sort of relationship get started in the first place (imagine trail riding etc. with a loose mini along.. not so good).
Jumping the gate is the problem you asked about. Since lunging on a line is out, simply stop lunging altogether. Ride.