Yep. First, I suggest you and they relax, do not panic. It should be only a minor inconvenience.
United has the responsibility to get them home and they will. Really, this is not a big deal. Contact United and they will find a way. There are literally hundreds of options for United to get them home from Lisbon to Chicago. Chicago is a gigantic United hub. Lisbon is a major city with flights to North America on multiple United partners.
Most likely United will put them on a partner flight (again, no big deal) from Lisbon to a major United hub in Europe (my guess would be Frankfurt, but could easily be Munich, London, or a dozen other cities). United has oodles of flights from Europe to Chicago. Add in all the United partners and you have a plethora of options. Your biggest challenge will be picking the option you want from all those that are available. So think about what would be a better flight (however you define that). Me, I like long nonstops or the fewest possible connections. But there are multiple considerations (how many connections, how long those connections are, etc.). By the way, TAP is just fine.
What I would do is to go online and look at what your options are if you wanted to buy a new ticket from United (on United or a partner or some combination) tomorrow from Lisbon to Chicago. You will find literally hundreds of ways to do this. Look for one that you want, like with just a single connection (preferably in Europe). Ignore what the price would be - there is no price, the price doesn't matter. Yes, really. Ignore what the price of a new ticket would be, it is meaningless in this case. Important: Jot down the details for those flights you want. Then call United, explain the situation, and ASK them for the specific flights you want, providing the details for the flights you picked. It doesn't matter what the flight would cost, United won't care and you don't need to either. You can actually get a BETTER flight (I do this all the time - flight cancellations can be a great opportunity!). Just be polite, ask nicely, have your act together, and know what you want to ask for. And above all, relax, this is not a big deal, it happens millions of times every day.
Good luck and do not worry!