Is is wrong or illegal to just lie? I was asked this by an external recruiter once and I just told him the salary I wanted to make, and it ended up working out.
So, don't lie. Just refuse to tell them your salary history and talk about your expectations instead. If that negotiating approach causes you to lose that job opportunity then you were probably asking for more than they were willing to pay, and you probably weren't going to get it anyway.
Always add 10-20%. If they like you, they will offer you and you can negotiate from there.
It's not even really a lie if you consider that any equity you may have has fuzzy value.
They'd expect you to be wanting an increase in order to move?
I think, they believed me but weren't inclined to pay me that much.