If the lender really wanted to refi your property it would have investigated further and determined that you're not liable for the taxes. Consequently, what the lender is really doing is looking to avoid telling you the true reason why it's denying the refi (e.g., you locked your loan a lower rate, and the lender is now in a losing money position).
You could offer to buy a surety bond and record it in favor of the county for the amount of the tax liability. That would prevent the lender from losing on the deal. Or, you could offer to pay off the tax bills. If the lender still refuses, then that would pretty much prove my hypothesis: the tax bills are not the reason for the denial.
If you want to sue the lender for misrepresentation, you need clear evidence that the lender is using the tax bills as a red herring to deny your refinance. So, call their bluff and see how they respond. If they tell you, "Okay, under those conditions we will approve the loan," then you can either accept, or you can walk away and try to find a different lender.
But, I'm betting that this is all about an increase in rates and the lender doesn't want to admit that it can't make the loan at the rate in the GFE
without losing money.
Please let me know if I can be of further assistance.