Do you want to visit Erfurt?

I haven't needed to try this for several years, but you may be able to book those trains on one ticket, which may be cheaper (particularly if you can get some of the route to be on regional services) by specifying a stop over in Erfurt, of 12 or whatever number of hours.

Also maybe it's a typo but you say the flight is at 1241 and the train is also at 1241? Are you sure that flight is not just the train on an LH codeshare?

Either way 3 hours is overkill in ordinary circumstances