Hi
There should be no lag what so ever with a supercharger, its allways on boost because its mechanically connected, theres no spooling up as like a turbo
the supercharger is directly connected to the crank via a belt, so its allways creating boost proportianal to revs, the F-type uses a twin screw supercharger, which is perfect for the job and should create boost all the time
if you have lag or its hesitant, there may be a issue, could be a split hose or air leak or even a slipping supercharger belt
cheers
Joe