Hi T_G
This could be an interesting and very worthwhile project and using the lathe drive would certainly save space but at the expense of having to assemble it every time you want to cut something. If you are like me and only use a tiny fraction to the lathe bed, usually, you could semi-permanently mount your hacksaw at the extreme tailstock end and connect it to the chuck with a removable drive shaft when needed, of course you would have to be able to easily remove the tail stock.
Some other suggestions that might be viable alternatives:
Make some sort of frame to convert your hand held bandsaw into a bench top machine....
Make a bandsaw that would fit in the lathe, the general idea is you put the drive shaft in the lathe chuck and clamp the work to the cross slide.
Buy a circular cold saw blade and make an arbor for it so that you can clamp your work on the cross slide and use the lathe as a cold saw.
Cheers
John