My brother did this exact same route last year when he came to visit, and all the connecting passengers from FLR got bounced at the gate for being late - the plane clearly still being there. LH chose to put all of them (over 10) in one of the FRA hotels rather than let them board. So I'm not sure I share the overall optimism about the connection. It can be a bit tight. They were delayed perhaps 10 minutes, but it was enough.
FLR-FRA agents are italian, that's all. You have to know how to play the game with them. Helps if you are italian
I once took an LX flight out of FLR with a small carryon (really small) and a small documents bag around my neck. Initially it was "Oh, can't do that, bla bla" I'm like "What do you want me to do, my laptop's in my carryon bag, no way I can check that in", you know, do some hand waving, so she goes "OK, let me take a look, see what we can do, why don't you pull your laptop out and hold it, then your docs bag fits in, let's call that one bag and we're done"
Absolutely priceless. I miss it sometimes.