Saved Lot to Bin, Portrait Paintings Missing

Try going into the old save again and first taking all the portraits off the walls and placing them in one of the Sims' personal inventory, and then saving the family and the lot again. I don't even know if this was intended to work this way, but I know that it at least sometimes does. I've used an old active household from my library in a completely different save, and I was pleasantly surprised to find the portraits and still lives one of them painted preserved in her personal inventory.

I agree with PalmArrow. I would also consider using a new house (because it might have been the cause of the bug - you could build a clean replica though).

Be sure to take the urns and gravestones of all past relatives in the inventory of the living relative. If they're not on the previous world's lot, then go to the cemetery of the previous world through 'manage the dead' whatever, and get them. Otherwise they won't show up in the family tree in the new world. If there's living relatives that join up some of the relations in an important way in the old world, then maybe you could move them in to your household in the old world and take them with you. I don't know if this is affecting the family portraits. It shouldn't do? That would be a very strong connection.

I'm not an expert on the paintings. Palm Arrow's suggestion sounds like the best strategy to me. My sims moved into a new house in their new world so all of their items were in their inventory anyway to be able to say what happened to their paintings. I just know about the urns and family tree thing. One of my sims took the grandparent urns but the parents were still living in the old world and didn't come along, so when the grandparent ghosts came out they didn't know who she was and didn't show up in her family tree.