There seems to be another option ...
If you check bahn.de they offer a bus / train connection that runs every two hours with total travel time between 3:01 and 3:09.
It involves a direct-bus from Luxembourg to Saarbrücken and connecting there to various ICE/TGV/RE for Mannheim. Discount-fares start at about 19,90€ if ICE/TGV are involved.
If RE from Saarbrücken to Mannheim is involved they don´t offer a discounted ticket at bahn.de because no higher class train is involved in the trip (but it´s still possible to buy a different and cheap ticket if you know the range of offerings ...
e.g.: Rheinland-Pfalz Ticket)
Btw.: If you buy the Express-bus ticket separately it costs 8,-€ ow and if you add the Rheinland-Pfalz-Ticket at 24,-€ its still cheaper in total than the full-fare ticket that bahn. de sells for the itinerary without ICE/TGV ...
The Express-Bus between Luxembourg and Saarbrücken is not related to Flixbus.
Just an additional note: Although Mannheim is in the state of Baden-Württemberg (so outside Rheinland-Pfalz) Mannheim Hbf is covered by that ticket which is an official concession (I can provide a link to official details if needed - albeit availlable in German only)