My x girl friend and I purchased a home in georgia together. She left and I am paying the mortgage.

If you can't pay the payments, how would you begin to pay the significant cost of a lawyer?

Additionally, absent a contract between the two of you, what basis would you have to sue?

You actually have a different problem, which is addressing your liability to the bank. You may want to see a lawyer to address that.

If you and your ex had a specific agreement about how to divide up the mortgage payments, you could sue her to force her to pay her share per that agreement, but you will have to prove the specific terms of that agreement, and if it isn't written down (and if she denies it) then you may have difficulting proving what the agreement was. Moreover, even if you eventually prevail, the mortgage lender is not going to wait for that suit to be resolved, and if you cannot make the mortgage payments in the interim, the mortgage lender will likely take steps to put the house into foreclosure. While I cannot create an attorney client relationship over the internet (and without reviewing the documents in your case and discussing the facts in more detail), I'm forced to agree with the other response that you might begin by having a conversation with the mortgage company about what help they might be willing to give, and if you haven't taken steps to try to sell the property, you had better start! It would be best to consult with an attorney before taking these steps.