The nearest train stations are Langen am Arlberg and St. Anton am Arlberg; both are on the Westbahn route between Zurich and Vienna. Lech can be reached from the train stations by bus or taxi (approx. 20-30min). We will gladly take care of a corresponding booking!
The nearest airports are: 
Innsbruck (1:25h), 
Altenrhein (1:10h), 
Friedrichshafen (1:30h), 
Zurich(2h), 
Munich (3h). All are accessible from many airports in Germany and internationally. We are happy to arrange a transfer to Lech, by Arlberg Express bus directly to Lech or taxi.