What is it called when a client licks/ sucks on the lady's tits?
nursing?
I read the PLEASE READ/ abbreviations and did a search with no results

thanks!

Licking and sucking on a woman's breasts is just licking and sucking a woman's breasts.

Is she lactating? Oh, well, then, if she's lactating, then you could just imply that they are into lactating women, as I don't know that there's a 'word' for it. However, nursing would then be appropriate.