Do LARS units prioritize aircraft in IMC outside CAS?
No, individual controllers may.
Do remember that LARS and even radar services from non-LARS units is usually a secondary task to a controllers primary one which is providing a radar service to aircraft inbound and outbound to that particular airfield. Even though they are 'there' they may be too busy to do it.
Lakenheath is not a designated LARS unit and you heard yourself that the controller was busy providing a service to LKH/MLD ins and outs.
VA