I would put a pin through the hole with the proper clearances. The include a contact condition with friction between the pin and the hole. Otherwise the stresses on the lifter will be way off.
You can then apply the load on the ends of the pin. If you don't care for stresses on the pin, make it rigid so the bending does not cause edge stress on the hole.
If you want to simulate lifting you need to include standard gravity and constrain the ends of the pin instead.
You don't want to constrain the lugs because then you are over-constraining the structure as it won't be allowed to flex properly. As a last resort you might try a remote displacement in the center of the holes with deformation on. If the lifting is done with a bolt, then a coupled condition on the remote displacement would do the trick also.