Nice little gun in overall good condition. The rear bottom lug has been peened to tighten the action but with the forearm off, the action still has some play side to side....with the forearm on, the gun is tight. Should I be concerned for now? and what most likely is the fix?

The fix is a bigger hinge pin; if there is room for one. Or a shim to take up the slack, which is not permanent of course. Or building up the barrel lug. In any case, it is not usually good idea to shoot a loose gun as that just hammers them looser.
The forearm makes it seem tighter but that is deceptive. I suppose you could shoot it a few times, but for actual use, it should be fixed properly.
Belgian gunmakers were not keen at case hardening, as you see.

First, I am not an expert, but I have learned a little.

It really needs to be looked at by a pro. Tightening by the hinge pin or hook may be fine, but it may also need the lumps worked on. In a perfect world, the front of the lump rides on the frame and takes pressure off of the hinge pin. In theory, the hinge pin is a rotation point and isn't totally load bearing.

In a low pressure shotgun, tightening the hinge pin or hook works fine. In higher pressure rifles, more should be looked at.

Jeremy

right.