My mom wants to add me to her deed. She still has a mortgage payment. In the event of her death, will have to give up the house or do I just continue paying the mortgage.

Does she have a will?

You could continue paying the mortgage.

If she wants to add you to the deed, she should deed it to you and herself "as joint tenants with right of survivorship, and not as tenants in common" (if allowed in your state). Because if it were titled to the two of you as tenants in common, when she dies half interest would remain in her estate. If she leaves you everything in her will (or you are her sole heir under the laws of intestacy in your state without a will), it may go to you eventually, but it would have to go through probate first. JTWROS would be better because no probate would be necessary.

Your title says she already added you to the deed, but then you say she wants to.
A lender, as a lienholder, can refuse to allow someone to be added to a deed.
Your mother should check with them to see if it's OK. If it is, it's a simple matter of going to the deed office and filling out and filing a new deed, with a fee.

Actually its not that simple as there may be tax consequences to giving you a gift of a half ownership in the property. I would suggest your mom consult an estate planner to see the best way of doing this.

Agreed, in basics, yes, that is what happens, you are added to the deed, and if worded properly, you just continue making the payments after she dies.

but laws vary on where you live, and normally any changes in the deed will require the lender to approve,

Depending on the equality, in the home, once you are added, she has given you a gift of that value, which has tax issues.