If I got your details right you are arriving on LH in first class. Then, given your flight is on time, you even should be able to use the additional time at FRA to take a shower in LH's First class lounge before collecting your luggage and boarding the train.
According to the response to my other thread about arrivals, I got the impression that using the lounge to take a shower would mean we'd be taking our chances with our luggage. Is there a reliable way to ensure that it is secured while we're using the first class lounge at FRA?