Depends on the waterlift. Many are made of plastic that don’t play nice with adhesives and that could be why yours has come adrift.
But as others have said, before gluing wood into boat as a base, ensure there is enough room not only to fit but also to have access to secure.
I have just replaced both my shower sump
assemblies and used my own “custom” wood platforms, glued into the hull, to mount them on. In my view the better method.