The builders have ____ the last row of bricks along the garden path.

Explication

After have the verb needs its past participle, and the object — the last row of bricks — shows that the verb is the transitive lay — laid — laid, whose participle is laid. Lain is the participle of the objectless verb lie — lay — lain, which can never take an object at all, and the base form lay leaves the perfect construction unfinished.