The bird in your photo isn't a Lapwing, but there probably were quite a lot of them at Lakenheath. A few years since I've been. Your photo shows an Oystercatcher.
It's a great reserve. Sadly the last place in the UK where Golden Orioles used to breed (in the poplars). Did you manage to see the Bitterns or Cranes, both of which do breed there along with birds like Marsh Harriers, Bearded Tits, etc.