I can help, since I have one as well. The lever on the left side, as you've already realized, allows removal of the barrel and forearm. The one on the right side allows removal of the lockwork. Unscrew the lever on the right side, remove it from the receiver, lower the breech block completely, pull down on the trigger guard while holding the cocking lever down fully and the action should drop down from the front and out of the receiver. Be careful about the pins (which are true pins, not screws) that hold the various action parts together as they sometimes have a predilection for falling out or at least sliding somewhat, and the action won't go back together if they aren't flush with the parts they hold in place. Does yours have the split frame (the bottom of the receiver forward of the action will be split) or a solid frame?
These are actually pretty simple little mechanisms and all of the various small frame Martini actions I've owned have been excellent shooters.
A fairly large percentage of these rifles were lined. Usually the liner comes to the muzzle and if you look carefully you can see the seam between the liner and the barrel. You'll often find the words "Parker Rifled" on the muzzle end of the liner. Not related to the Parker Brothers of shotgun fame, this Parker seems to have been a manufacturer of sights and other similar things for target rifles of the era.
Before you decide to rebarrel, take it out and shoot it with some good quality ammo. You might just be surprised how well it shoots.
