Removing JWM won't help anything - JWM has no influence on the menus shown by other software.If I were to simply dump jwm, would xfce use it's own list?
I think the problem is that XFCE is using its own (i.e. different from the standard Puppy one that JWM would use) menu structure. And I think lxmed is using its own menu structure too (from memory I think what it shows in your screenshot is the standard LXDE menu structure, not the standard Puppy menu structure).
I have seen references to using lxmed with XFCE, but I'm not sure how to make it look at a particular structure. Looking at this I'm wondering if maybe it isn't even possible (without modifying lxmed): http://lxmed.sourceforge.net/help.html#category