You’d have to verify the parts on the exploded view Grindstone Cowboy linked to are still present in your own lathe Dan. As others have said, those aren’t meant to clamp the carriage down in any way, there simply in place to prevent any lifting of the carriage. If my interpretation of the drawings are correct, then it’s part #27 at the rear of the carriage and #140 at the front that are designed to prevent excess lifting at either end of the carriage. A carriage lock would be used when facing a part to prevent the carriage from being pushed back.
On a brand new lathe, there would be a very small clearance between the lip of #27 & #140 of only a very few thousandths of an inch and the bottom of the lathes bed ways. That allows the carriage to travel longitudinally along the lathe bed without any binding. The more bed and carriage wear there is, the more clearance there will be between those plate lips and the bottom of the lathe bed ways. However you still can’t re-machine the parts to tighten that clearance any more or you will have binding at the far less worn tail stock end of the lathe bed. And as others have already mentioned, I can’t visualize why your seeing even by eye the carriage lifting under any cutting loads. Something definitely isn’t correct.
Unless there’s parts missing or an incorrect reassembly I can’t visualize. The only other possibility I can think of is your lathes upper way surfaces and bottom ways on your carriage are extremely worn and allowing the carriage to rock up and down. And if that is the cause? A full lathe bed and carriage way regrinding with possibly additional scraping might be the only fix. Even that causes further issues with realigning the lead screw further down to then match the half nuts new and lowered elevation position. Depending how much grinding was needed, something like a Moglice, Turcite, Rulon product might be used to build the carriage ways back up. But likely only a machine tool re-builder could advise you properly about what might be required.
Pulling the tail stock and removing the carriage, then using something like a metal yard or meter scale as your straight edge and held tightly against the side of the lathes front V way and the same on the rear flat way against the mostly unworn tail stock end should give you a fairly good indication of the amount of bed wear you have at the head stock end. Feeler gauges between the worn bed and the edge of the straight edge would get you a fairly close estimate of the amount of bed wear. There’s no simple or easy method of gauging the amount of wear on those bottom carriage way surfaces that I know of. And unfortunately, bed wear of that amount would also mean the tail stocks bottom way surfaces, cross and top slide ways will also need re-grinding and maybe scraping.