Final answer:
The superior gluteal artery is the vessel that passes between the lumbosacral trunk and the ventral rami of S1, providing blood supply to the gluteal region.
Step-by-step explanation:
The artery that passes between the lumbosacral trunk and ventral rami of S1 is the superior gluteal artery. This artery arises from the posterior division of the internal iliac artery and exits the pelvis through the greater sciatic foramen above the piriformis muscle. It is responsible for supplying blood to the gluteal muscles and other structures in the region.