Unless the collet is custom made with a step ground into it to serve as a case head depth stop, you won't get uniform case position each time. That means you will have to be individually measuring and then trimming off the difference calculated. It will be a painfully slow process. Even then, it will only work well on rimless case heads. The others need a step ground into the collet anyway, because a rim or a belt, which are the widest part that the collet will grasp, don't have enough length to straighten out in the collet, so they won't run true without that. Then you need a cutter to trim with that won't pull them loose from that precarious hold on that narrow band of brass, so you'll end up buying the same piloted cutters several of the commercial lathe trimmers use.
Where you might get some mileage out of your lathe would be by chucking the Lee trimmer holder is in it, then using their cutters. About $5 or $6 for each half of the gear. Run the lathe at about 150-200 RPM or so and insert the cutter by hand. Let the lathe engine to the turning part, which spares your fingers.
By the way, I don't know what you are planning to load for, but be aware that cartridges fired below approximately 30,000 psi will shrink rather than grow with use. There is never need to trim .45 ACP, for example, as long as you are using a taper crimp die. For roll crimping lower pressure rounds, you may want to trim cases short just once to get them uniform so the crimps will be uniform. That usually means trimming slightly shorter than normal, so you might find you have to grind a little off the Lee "length gauge" part of their trimmer to get where you want to go with it?