https://www.flightstats.com/v2/fligh...ing/LH/819/GOT

From the last 60 days, LH189 has been cancelled once and the maximum delay has been 23 minutes. Based on these statistics, I would be confident in making the flight.

Of course it can always happen that something goes wrong and you miss the connection (even with longer connecting times), and LH would rebook you and provide a hotel and food. My advice (which I think you already are considering) is to have a specific plan B in mind (or check on your phone while waiting for rebooking), which you can request if the proposal from LH isn't what you want.

Frankfurt is quiet at that time, and I would only consider running if you are really late. The boarding time given is when boarding opens - you just need to be at the gate 15-20 min before departure.