You could always do what I do... skip FLS altogether and just use the Lee Collet Neck Sizer Die, which requires no lube...
If you like to run through a tumbler you could use the universal decapping die, then reseat primers, tumble, size w/ Lee Collet Neck Sizer, charge and seat?
I guess I'm not sure what you figure to be gaining by doing things in that order, but to each his own... I don't even bother tumbling or removing primer residue anymore.
Neck size, prime, charge, seat, BOOM, neck size, prime, charge, seat, BOOM, ad infinitum so far as I can tell.
The rifles I've used this sytem on haven't "needed" FLS for something like 15 loadings? I'm pretty sure I have really old '06 cases that have been loaded close to 20x w/out "fatalities," although around about that time annealing of the necks is in order. I say "pretty sure" cuz back when I was carefully prepping each case I wasn't as careful about keeping track of lots and number of loadings per case... it was all once-fired brass from factory-load shooting heathens... I mean, friends.
