First, Lee's FL size die is no different from others.
Neck sizing, correctly done, means you make no change to the case body. The less body taper a case has, the less likely it is to work. If you can run your case into the die so the neck will be sized to the base of the loaded bullet with no die-to-body contact, you will be fine. If not, it won't work. It's somewhat rare for it to work well.
Test your die and a fired case by painting the full body with a dark color "dry erase" felt tip marker. Run the painted case into your sizer to the depth you wish and check for a hard body rub mark at any point. Do the case insertion in a series of small steps, withdrawing it fully each time to check for the rub, otherwise you may get a very hard stuck case.