Is there a quaint-sounding/archaic dual to address women a la "[my] [good] sir" jovially in casual conversation? I can't come up with an expression that doesn't sound like a moderately intense term of endearment (e.g. my [fair] lady). Can you even sound quaint but still be modern?
How "lady" is going to be received really depends on your audience. That said, some options are:
A lot will depend on context, too, as well as tone.