You'll need to see how the carriage is. My first machine sat on a carriage, so it could fit on quite a few frames. I had it on a wooden Grace frame, and like other have said, I would not put a heavy LA on that frame.
My HQ has the front/back carriage wheels built on the machine, so it is very specific about what type of carriage it can mate up with. And the HQ carriage that it works with has a very different wheel system than the Grace did, so without putting a different rail system on the Grace frame, it would never work.
My DH has the metal working ability and tools, so I'd probably buy the 14' frame if it was priced right, and modify it to fit.