There are now two distinct travel options when taking a train from München/Munich to beautiful Lindau on the shore of the Bodensee.
(1) The newly improved express train service on which very smart EEC traina now complete the journey in under two hours.
However, they arrive at a new station, Lindau-Reutin, which is a 10-15 min walk from the lovely island on which the old town is located.
Though an option is to connect there for a train to Lindau-Insel station, which lives up to its name as it's on the island.
(2) Regio trains, operated by ALX and not by DB, still provide a direct service to Lindau-Insel station.
If you book ahead you can save money, by taking the express trains, but if you will be buying tickets last minute at the station, the Regio trains will be the cheaper option.