I dont know about the lowest thats ever been tried but here in wisconsin the legal min. limit is 100lbs for a crossbow with a min. of 14" arrow

for vertical bows its 30lbs with a min. broadhead width of 7/8"

my sons bow is 30lbs(maybe a little under)and its surprisingly capable of flinging an arrow with some force and actually gets pretty good target penetration, I wouldnt try 30 yards with it but out to 15, maybe 20 yards max(with a good shot) hissetupwould take a deer