There are several collet attachments for Logan lathes on eBay right now if you are considering looking for one. There were a couple that use a handwheel drawbar and there was one that uses a lever drawbar. I don't care for the lever type as you have to remove the gear train cover in order to mount them.
Another option would be to simply purchase a new 3AT spindle adapter for about $30 on eBay, then make your own thread protector and handwheel type drawbar. Then you would be all set. You could make your own adapter, but they are usually ground to final dimension, plus they have a small internal key. You would need a good working drawing or an adapter to copy if you were to make your own.
Keep in mind that I am not saying that you should do that, I am only saying that you could do that if you wanted to get set up for doing collet work. I like using collets when I am making things from smaller sizes of round stock, concentricity is pretty much guaranteed and the collet will hold it better than a three jaw will in those small sizes. With some of the smallest sizes, a collet is nearly the only way to go.
You can use your collet holder in the four jaw chuck, but will need to dial in your part each time you mount one since to remove the part you will need to remove the block from the chuck so that you can get at the nut on the back. On second thought, you could remove the four jaw chuck from the spindle to get at the nut, but that is almost as much work as just dialing in for each part.
Whatever you choose to do, you will probably at some point wish that you had the rest of the collet equipment and a full set of collets, especially if you make small parts for firearms or model engines.