Thomas,
You'd better print your boarding pass back at home before flying to BEY.
BEY is a small airport, but arrivals and departures are seperated. There is a transit channel, but I've never used it. However, AFAIK it will be hard for you to find a counter that prints your Lufthansa boarding pass in the transit area - that kind of thing may work for MEA flights and some others, but I doubt it works for LH.
Which would leave you only with getting out and in again: make sure you are among the first off the plane. You then head through a short corridor towards immigration. If there's a queue at the "foreigners" counter and no-one at the "Lebanese passports", just go there, they don't mind too much. After that you go through the baggage claims area with a Duty Free that's nice if you're into cigars. After that you head out, arriving into a complete zoo (summer is the high time at BEY, all flights are full, and travelers usually arrive with about 3 tons of luggage each and are being expected by delegations of at least 74 family members). Go through the zoo and walk up the stairs to the departures level. There you have to go through a first security screen, which sometimes is a little crowded (5-10 mins max). LH check-in is in the West departure area. However: AFAIK, CKI closes 60 mins before departure, so that makes your turnaround difficult.
The lounge is the MEA lounge on the upper level, which is okayish. The lounge is spacious, but food and amenities are mediocre. If you want to use free WiFi, connect to the "MEA" network (not the other one which is advertised everywhere). Although the welcoming page of the "MEA" network tells you something about payment, it's in fact free. Just browse.
Lufthansa flights to BEY are a real pain during summer. They're always packed to the last seat, and pax are of the big family/fridge in their hand luggage/jumping around all the time-type. Seats are uncomfortable for such a long flight (to compare: Air France uses their B777-300ER with real business class seats - the only route where I prefer AF, if you remember the AF war stories I told you at the ZRH Stammtisch).
Hope the money saved is worth the hassle ;-)
Let me know when you're flying, I'll be going myself on that day flight mid-August (PM me).
Best