This question is perplexing. So it is currently being repaired AND the same company wants to buy you out of the lifetime warranty?? I am taking this to mean that a) this same company repaired this duplex in the past; b) they are repairing it now and c) they don't want to ever have to do so again.
Honestly, I've never encountered this type of scenario before. Depending on the scope of the current repairs (and I would definitely get another company to evaluate the foundation), I might let them buy me out for a pretty penny and then ABSOLUTELY go with another company for this specific repair (if indeed you need one at this point in time). But the situation you describe just seems shady and weird to me.
Before you do/sign anything with this particular company, I would strongly advise you to get a structural engineer from a well-reputed foundation company to come and evaluate the situation. It would cost you little (and, if you play your cards right, possibly nothing), and it could really save you some headaches and losses down the road. You might also ask the engineer that the company sends out what they think of such a request.
As far as how much not having a warranty will affect sales price: there are so many variables, so this is difficult/impossible to answer without more information. Parts of Austin, for example, are really reputed for foundation issues (i.e. the east side). Many buyers in these areas are usually prepared to put up with a little shifting. BUT if the foundation has shifted significantly, it becomes difficult (if not impossible) for a potential buyer to get a mortgage until it is fixed. This could seriously hinder you on re-sale and will certainly scare away some buyers.
Generally, a life-time warranty certainly reassures buyers and adds value, so it's always better to have one. That said, the lack of one does not (in the Austin market, anyway) necessarily kill the deal and/or mean you have to take a hit. However, it really all depends on the current state of the foundation, the state of the house, and the area you are in.
I notice from your profile that you are from/in Dallas? If the house is in fact in Dallas (and not Austin), then I would definitely ask some local agents there what their experience with selling houses with "imperfect" foundations is. Foundation issues play out differently in different cities and areas.
Good luck with this, and my condolences for having to deal with such a stressful situation.
Karen Pagani, Ph.D., Realtor
The Gill Agency