What gule should you use for a lap joint?

I assume that this is a lap joint in wood. If the lap joint is going to be exposed to weather outside, I'd look at a "marine" adhesive used in wooden boat making. Otherwise, any good wood glue applied to a clean lap joint, clamped, and allowed to properly cure over time should do nicely. The glue should be applied at room temperature in an even thin coat to both surfaces and then evenly clamped with several clamps along the joint for 2 days or so.