Can a doctor do a laparoscopy with a spinal tap instead of putting me out for endometriosis?

Usually not: Laparoscopy done with abdomen inflated(distended) to 30mm of hg(mercury), at that pressure need respiratory support ( mechanical ventilation) so spinal anesthesia is not a preferred method.

Not recommended: Laparoscopy requires gas to distend your abdomen and a tilting of your body towards your head in order to see the pelvis. This may prove too uncomfortable. General anesthesia is very safe and easy to reverse once the surgery is over.

Possible but not recommended: Spinal anesthesia or epidural anesthesia is possible but not recommended for laparoscopy. The discomfort with the insufflation of the gas may be too much to bear when not asleep. The manipulation of the pelvic organs may also cause tremendous pain. Also the tilting of the operating room table may allow the spinal anesthesia to travel further up the spinal column than desired.