If the carriage lock causes the crosslide to bind I'd say that's probably due to distortion. Unfortunately, with import machines, you can't always trust that the scraping and fitting is 100% (although for the most part it's decent).
Even a small area around the lock screw that lacks proper contact could skew the saddle a bit when the screw is tightened, and it doesn't take much to interfere with the action of the crosslide.
Assuming your carriage lock is simply a screw that pulls a block against the underside of the bed like most imports (including mine) I'd say it's worth replacing both locks, the designs are a bit lackluster.
I think most would agree that you should not have these problems with a new lathe, so first you should probably determine the exact cause, and act thereafter.
Sent from my LYA-L29 using Tapatalk