The Lancaster Manual (publ Greenhill Books) has two pictures of the pilot's seat. One shows a bucket seat (so the pilot can sit on his parachute) and this shows what could be two straps on the back cushion of the seat, but it is not obvious exactly what they are.
On another picture there is a seat with a padded base (not suitable for the sit on type parachute) and this clearly has a 'Y' shaped strap running over the back cushion such that the two top ends of the 'Y' would go over the shoulders of the pilot. The end of the strap is not visible so it's not possible to see how it connects to anything.
Both pictures show a lever called the 'Pilot's Harness Release Lever' which is situated on the right on the outside front of the arm rest and attached to it (which can be raised so the pilot can get in or out of the seat). This lever looks like it could be hydraulically operated, or some sort of flexible rod, as there seems to be a flexible pipe coming from behind it leading round to the back of the seat.
There's also a photograph of the Flight Engineer's foldaway seat and I can't see any evidence of strapping in the vicinity.