Base security at most places is hidden and you won't have any problems if you're in the designated viewing areas.
Lakenheath has been quite strict since 9/11 though and you can expect attention from base police the moment you go anywhere off the beaten track there... I think there's a local nutter group who occasionally try to break in and protest too so it's not really surprising...
Common sense must be exercised. If you erect ladders against the perimeter fence then you will get negative attention from base security.
As with anything, if they come to talk to you just be courteous and friendly and you won't have any problems
