I've been using a large 20 gal shop vac (don't know the HP off the top of my head) and as mentioned above, it doesn't have sufficient air volume (CFM) either. It gets some stuff, but half of it still ends up all over the lathe, me and the floor.
So definitely, if you want to do it right, get a dust collector of some sorts. There's many low end ones in the 650 CFM range that will work pretty good for one tool at a time all the way up to some with several thousand CFM for handling several tools at once.