What does it mean to be "sixty-fortied"?

Solution 1:

The episode transcript earlier explains

LORELAI: This isn’t a singles bar, Mom. It’s a sixty-forty bar.

EMILY: A what?

LORELAI: Sixty-year-old men hitting on forty-year-old women, divorcees mostly.

When later the expression you mentioned comes up it refers to that:

EMILY: Yes, by sitting me at a bar where you practically forced me to engage in inappropriate behavior.

LORELAI: What?

EMILY: You let me get sixty-fortied!

As Silenius describes in the comments this is a form of transforming another class of words to a verb - or verbing / verbification. Therefore using the numbers as a verb by putting them in the right context and adding a verb ending.