Also LH from FRA. However, travelling on a Sunday as I did the last two times, it wasn't very full. I was through immigration that quickly that I had to wait a few minutes for my luggage. I stopped off to buy a SIM card before catching the AeroExpress, then walked dragging two bags to my hotel (new Mercure Paveletsky in Bakrushina St, same shared building as new Adagio apartments and Ibis) and was still there by 18:30.
Due to the never-ending excavations in Paveletsky Ploshchad, (why?) it still takes about 20 minutes to walk to the hotel, taking a detour right to the river to get an underpass across the street, then back along.
By the way, there is an Aeroexpress ticket machine in the international baggage collection area now (which I don't recall seeing before) so you can make use of your waiting time by buying a ticket.