They operated for many years after becoming a civil airport without controlled airspace handling both passenger carrying flights and freight without even a suggestion they might ask for controlled airspace so why would they need it now?
It's my understanding that the intention is to concentrate on freight flights when (not if) it re-opens and as controlled airspace requires a minimum throughput of passengers per year, determined by the D of T (who won't tell anyone what this minimum is), the airport wouldn't qualify anyway.
Before closing, they had their own approach radar service (APS) which also provided LARS; this would be sufficient in the future although Farnborough, who operate LARS just to the west of Manston, could easily cover the APS requirement using remote radars.