I have a LnL AP and a Lee Challenger Breechlock press and there is no way to convert one to the other. If you have the older
Lee Classic Cast press and not the
Breech Lock version, you can get a
1-1/4 x 12 conversion kit for the Hornady Lock and Load Bushings.
As with the LnL Single stage press, I don't think you can just swap dies from the LnL AP to the SS press without a height adjustment of the die or make a custom shim to slightly adjust the height from one press to the other, but that kit will work with any press that has the larger 1-1/4 x 12 threaded fitting on the press such as the RCBS Rock Chucker Supreme or Redding Big Boss press.