Few issues... First, do a search on PACER and do a party search for the person who has filed the suit. There are quite a few people who make it a life's purpose filing dozens of these suits. Generally, they have no interest in actually being a patron, they just go to different public places testing for compliance (I've seen things like "the handicap sign is 1" lower than required," "the ramp is 1/2 of a degree off requirement," etc).
They'll likely be represented by the same attorney(s) in each suit, who will likely be wanting some money for attorney's fees (you know, the "cash settlement" part of the equation). In the event you're up against someone who has filed many of these suits, then you may file a motion to have the person declared a "vexatious litigant." I believe most, if not all, of the jurisprudence on the issue is from California, so you're probably in luck [due to the frequency of filing, some dockets are getting clogged and some Courts are getting fed up]. If posed with losing a meal ticket and/or important life purpose, then maybe he'll back down. Likewise, his attorney may be inclined to advise him to back off, given the possible pecuniary loss.
If the person really is a prospective patron and isn't just looking for a free lunch, then I would suggest attempting to come to an agreement if possible and accommodate his needs. Why not increase the number of clients? Maybe you can turn it into a positive marketing tool.
That said, any settlement is only going to apply to the person filing suit... the next guy that comes in with the same issue will have the same cause of action... Ultimately, you'll either have to get a ruling that what he's wanting isn't covered or you'll have to remedy the issue yourself and bring the space into compliance. If you do settle, then be sure to make the terms confidential and, further, force the Plaintiff to not discuss the facts/allegations of the case with anyone else. It might buy you some time.
Second, if you have a lease agreement, then what does the lease say about the required changes? If this is your landlord's baby, then let him deal with it. In the event it spills over to you, then your landlord may be in breach. Regardless, your landlord cannot answer or make agreements on your behalf. It sounds like to me that you've got a card to play in that you have to be on board for the settlement or your landlord can't settle the case.
Third, the imposition of additional taxes (or costs) on your business ought to be a material consideration for all the parties involved, as well as the Court. If compliance really does provide some incredibly painful, marginal tax (or other cost) to be imposed, then you might consider making the argument. You will likely want to make a kitchen sink approach and throw every possible defense at them, presuming your credibility is not negatively impacted.
My suggestion is to hire a local attorney who is licensed to practice in Federal Court and who has familiarity with the ADA.