As long as clerks like that are not stopped, they will continue to harrass lottery customers.
I doubt that anyone could be held to their promise to split the ticket under these circumstances. If she's obligated to check your ticket anyway, then she hasn't given anything in return for your promise. What she did sounds like extortion to me.
How do you remedy this kind of behavior? Simple.
Don't nod your head or give any sign of assent, but smile real big and ask her name. Once you have it, say, "Thanks. You've just broken the law, and I'd start looking for a new job if I were you." Then report the incident to the lottery, in writing. I wouldn't be surprised if you didn't see her for much longer.