FRA is my home airport outside the US. With DL (and pretty much all non-*A carriers) you will arrive at the newer termianl 2. Distances can be quite long and there are no walkways. You have to take the AIRail (2 min ride, every 2-3 min) or much slower shuttle bus to LHs termianl 1. As mentioned before, neither terminal is the easiest to navigate, getting to and form the AIRail takes more time than the actual ride, and the sheer number of counters in terminal 1 in a typical, cluttered 70s layout can be confusing.
LH requests a 2-3 hour advance arrival and sometimes, especially if you have not status on *A to get to the elite counters, it can indeed take a long time. I have gotten away with 1h advance arrival for intra EU flights, but I would not recommend it.

Terminal 1, where you would have to wait if you play it safe for a longer connection, has nice shops, cafes and entertainment options. It is just build in a maze like structure, so make sure you get up from your late in time.

If things go smoothly (imigration, luagage) you might have your LH boarding pass within an hour. One little hickup and good luck with the LH agent. As mentioned above they do not care if your DL flight was late.

Also consider Air Berlin, Germany's WN wannabe. They fly FRA NCE.

Hope this helps.