You can use the chuck, but maybe not on a lathe.....
If the scroll function of the chuck still works OK, you certainly could use the chuck you have by making (or buying) a carving stand for it, and then use it on a workbench or in a banjo on the lathe to hold a piece for carving, texturing, or other embellishment. I use my Grizzly knock-off of the Vicmarc 100 chuck in my carving stand - it never leaves there.
I doubt you will find a standard adapter for 3/4"-10 to anything else; the 3/4"-16 tpi is the fine thread version of this threading size, and one used on older mini-lathes. As noted above, you could have a machinist work on new threading or making a custom adapter, but that might become really expensive, really fast (...the Harbor Freight chuck might not be worth the extra expense!). BTW - The Oneway Live Center has threading on it for the cone, and other accessories and is 3/4" x 10 tpi (coarse threading) - I have never seen or heard of spindle threading of 3/4" x 10 tpi on any lathes, old or new.
There are a few mini-lathes still around with 3/4"-16, but nearly all new ones have now moved to 1"-8tpi. Adapters for 3/4"-16 sizes can be found from Bestwood Tools (which, BTW, also sells an excellent carving stand adaptable for chucks), Grizzly, Penn State, perhaps Woodcraft, Craft Supplies [
http://www.woodturnerscatalog.com/p/5/-/25/112/-/5837/Turners-Select-Spindle-Adapter?term=spindle%20adapter ], and probably several others.
Even if the Harbor Freight chuck is not used on a lathe it can possibly still be used if you choose to carve, pierce, texture, or do other embellishment methods needing a secure way to hold the piece, but NOT under lathe power. I use my carving stand (Bestwood) all the time, and my Grizzly chuck serves OK in this capacity. Even a home made carving stand would work OK if you can incorporate the HF chuck you have, and maybe get some use out of it without discarding it completely.
I hope this helps!
Rob