I have lap belts only in just about every car I own and they're just fine. Simple airplane style lap belts in the Mustang, Galaxie and Cadillac. Ol' Roy came with a set of lap belts but I haven't installed them yet.
The only vehicle I own with shoulder belts is the '79 F-100.
In vehicles like these, the primary benefit of seat belts is to keep you from sliding around on the seat and to keep you in place during evasive maneuvers or accident.