My sally's has both lye and no lye. Most asian BSS' especially the large ones have lye also have large tubs for "stylists" but I've never had a problem with buying the large tubs unless they've started checking for stylist credentials in the last few years
I read somewhere that some Sallys are only carrying no lye. You can always order them online if you aren't close to a bss that has them in stock. I'd order from Sallys or a reputable place. It would suck to order one that is no good.
Sallys sells the big tubs of professional relaxers but some Sallys employees will ask for your license and some will not. They sell them in the big and small tubs. The no mix relaxers are lye.
It sucks because my Sallys doesn't carry the big tubs but if I go to one closer to black folks they have the tubs and their ethnic hair products actually get a full aisle.