The USA has no concept of a transit passenger. You would have to get out and do immigrations/customs regardless as that is required for all arriving passengers.

I don't know about lounge access, but at LAX, you can enter any terminal with a BP for that day. And depending on whether you arrive after the T4/TBIT airside connector opens up within the next month, you won't have to leave airside to walk between TBIT and T7/T8, soon.