The closest airports to Lancaster are Newark, NJ and Philadelphia, Pa.
Both have rail links to Amtrack stations in the same cities, and both have rail links to Lancaster, Pa.
There is also Stewart Airport(Formerly an Air Force National Guard base) , but that does not have the rail connections needed to cover the ground travel component.
The rail link from Newark is going to pass through Philadelphia, anyway, and I wouldn't be surprised if the airfare to Newark, being a major hub with slots at a premium, would cost more than airfare to Philadelphia. Certainly, the railfare from Newark to Lancaster will be more than the Philadelphia-to-Lancaster railfare.
Both Newark and Philadelphia offer direct rail links from the airport to the respective city's Amtrak station; in Newark, it's AirTrain to Newark Penn Station; in Philadelphia, it's SEPTA's Airport line to 30th St. Station. It's not thru ticketing, however, and neither allows for pre-purchasing the air-to-rail ticket.
Stewart's rail links would be pretty poor even if they built an "airtrain" to the nearby rail service; you would need two regional commuter trains to get to connect with Amtrak (at either NYC or Newark, but that local commuter service only feeds into Hoboken, and offers a transfer in Secaucus to either NYC or Newark), and the regional commuter service has suffered from decades of neglect, because it's
owned by NY, but
operated by NJ - and NJ would have to upgrade the infra in their state to make an upgrade in the NY portion mean anything. And it's NJ that has neglected the infra; the NY portion is no worse than the NJ portion.
I'm also not certain you could get flights from Dallas to Stewart; while structurally the airport can handle pretty much any airplane in commercial service today, all the way up to widebodies like the 747 or L1011, its location and lack of ground transport links pretty much relegate it to being a regional airport.
Harrisburg PA would be a better choice than Stewart, but it's also a regional airport, and to get there from Dallas you'd have to change planes in Pittsburgh, Washington, or Philadelphia - and it'd cost about four times as much as just flying into Philadelphia.