If it sinks at the surface it will sink at any depth.

Unless you are talking about an upper layer of freshwater and a lower layer of saltwater that happens often where freshwater dumps into saltwater.

Water pressure if anything will compress the lure and increase its density. As the volume of the lure decreases, so does its buoyancy, as the buoyancy force acting on the lure is equal to the weight of water that is being displaced.