Not sure what you mean with the "Lee handloader."
IF you refer to the Lee hand press, then no, the LNL bushings cannot be used, that press is tapped for 7/8x14 for dies only. The Lee Classic Cast press will accept the LNL bushings and it's a great press too.
There are no "LNL" dies, per se. LNL inserts are screwed onto conventional dies to make them quick-change. If saving maybe 10-15 seconds per die change is an issue.