Looking at the lee quick trim die online I'm not sure there would be enough material to make the threads. You might be able to find another die from someone else that can be converted. If you were to take the die to a machinist to put the threads on it would be very simple for them to bore out a hole that the cutter on the trimmer could go into as well.
What might be easier would be to take the threaded mount off the Dillon trimmer and bore that hole out and then thread it in 7/8 x14 to fit the quick trim die. You would have to look into the actual numbers, and make sure that the length would work. If you dont already have a trimmer you might be able to find someone who has one that is burnt out or even try Dillon as they might be able to sell you the individual part.
I ultimately went away from the trim die for a few reasons. I was working on my project at home as well as at the shop so I could get more done and once when moving my press I broke one of the trim dies. I bumped one of the trimmers and it broke pretty easy. Then when I went to purchase another one the only place that made them was out of stock. Now there are more people that make them but I just figured that if there is a possibility of something breaking and my not being able to replace it in a timely manner then I had to have something else. Also I found that with the trimmer being suspended above the die and only open space between the two I was able to clear chips better.