Most of the turning tools I have made are from steels like W-1 and 1095. A turning tool has to take and hold a really good edge. I wouldn't use 5160. It would work, but would need constant edge dressing. 1" W-1 drill rod would be perfect to forge a 40-50mm gouge out of. Other good choices would be T-1 and M-2, and CPM M-4. These would need professional HT, and do not forge easily.
If you have a swedge block available to use, it will be your friend when forging flutes. If not, you might want to make a simple swedge hardie. (BTW, 41XX steels make great hardies, and can be hardened to the mid Rc30's)
If using W-1 or 1095,you can do your own HT.
Make the tool and have your friend check it out before hardening. He should hold it on his lathe and see how it sits and feels. Once all the end angles and curves are adjusted, cycle heat the end 6" ,finishing at 1200F. Then austenitize and hold for 5-10 minutes, quenching in fast oil. Temper twice at 400F. Sand it up to 400 grit, then draw the shank with a torch. Start at the tang, and go toward the cutting edge ,watching the colors walk toward the end, and stick it in water to stop the temper when the straw color is 1" from the edge. This should give you a cutting edge around Rc62-64 and a tough shank.
Only other advise is to make it BIG and ROBUST. The bigger the better with a bowl gouge. It has to be able to absorb the force of the cutting without any chatter. I have seen 50mm bowl gouges 4 feet long with 3/4" thick shanks. The handle is usually about 2-3 times the length of the exposed blade. A 50mm bowl gouge is about 36-40" OAL, including handle. Make the flute at least the last 4-6" of the gouge, and round the bottom of the shank back all the way to the taper toward the tang. The tang needs to be at least as long as the shank. So, for your size (40-50mm gouge) that would be a 24" piece of stock with 10-12" of shank, a 12-14" tang, and a 24-30" handle. The owner will probably want to turn his own handle, but it will probably be about 1.25-1.5" round ( at the widest places).A good size ferrule is a must on the handle.
Stacy