The FRA Arrival (Welcome) Lounge is not the only arrival service. Arriving First Class passengers can actually use the FCL as an arrival lounge in FRA and MUC, so they don't have to use the FRA Welcome Lounge unless it is more convenient. One problem of the FRA Welcome Lounge is the fact it's only open until 12:30pm (last admission). It will be no use for the OP of this thread, for example, whose flight from NRT is scheduled to arrive in FRA at 2:30pm.

There's no need for LH to arrange a day room at the Kempinski for First Class passengers who have flights to another destination later on the day, as they can spend their time in the FCL. My guess is that the Kempinski offered LH a deal to use otherwise vacant rooms during the day for a small charge. It is certainly good publicity for the Kempinski.