I'm currently consulting on a project with Alaska Airlines and I can tell you that it's complex, but not in the way math or physics is complex. There are just a
lot of details and a foundation of legacy going back to the 60s. For example, the details of EDIFACT[1] leak out far and wide, and the codes are still essentially the same. For example, the codes on a boarding pass[2] are essentially unchanged.
I don't know for sure that Lisp would be required (for the functional aspects?), but I can see the appeal.
As far as lack of documentation, it's not really any worse than any other field. Sometimes there's huge, detail-filled document from some organization like the IATA, with lots of revisions, sometimes the documentation is out of date, and some times it's missing. The worse problem is that all the original knowledge retired with people long ago, and the game-of-telephone version we have now is also walking out the door, because of pandemic-related disruptions in the travel industry generally.
It's a huge industry, and airlines are motivated by both profit and regulation to accommodate all kinds of things you wouldn't necessarily think of.
Speaking of profit, yes, extra bag charges, seat changes, and upgrades are explicitly revenue generators. They aren't just covering the extra cost, airlines will upsell you a variety of extras (would you like fries with that? some dipping sauce maybe?) in pursuit of profit.
1 https://en.wikipedia.org/wiki/EDIFACT
2 https://www.thesun.co.uk/travel/5703214/boarding-pass-codes-... although the trend towards electronic boarding passes and scanners means the letters and numbers are disappearing into the barcode or Aztec code.