The nearest railway station to Lakenheath is Thetford, which is between 90 minutes and two hours from Kings Cross station in London. You can check times and book tickets from London to Thetford at www.http://www.firstcapitalconnect.co.uk or one of the national UK rail sites like The Trainline or Loco2. Booking tickets in advance may be cheaper, but you will need to buy a ticket if you miss the train you picked because of a delayed flight.
You can see details of buses from Thetford to Lakenheath at http://www.coachservicesltd.com/timetables-maps/?serviceid=1755. The bus station and the railway station in Thetford look as if they may be some distance apart so don't plan on a tight connection. Or get a taxi from Thetford.
The most direct route from Heathrow to Kings Cross is to travel on the Piccadilly Line underground, although it can be very crowded in the morning peak hour.