Don't know if this is still an option but at one point Lufthansa was hiring American instructors for its flight school in AZ. After a few years there was the opportunity to go to Germany and work in their training center there. It was not a route to flying for Lufthansa but it could possible open other doors.
As for working in Europe, as Typhoonpilot mentioned, getting the right to work can be difficult. Marrying a girl from Europe helps. Some countries do allow citizenship to pass down. If you have a parent or grandparent who was born in Ireland you can claim citizenship (I was fortunate to have a grandparent born in Ireland so that is how I landed my Irish citizenship). Germany has a path to citizenship through ancestry and I know someone who has done it through Italy as well.