Thanks for all the insights... well, I changed my ticket to TLV and have now 5 hours, the only other option I had.
The transit situation does not sound very encouraging, I had previously problems at TLV, when I stayed couple of times for 2 days on business. I was questioned for over an hour in front of the LH check-in, why only 2 days, etc. and believe me, I do not look suspicious and have a normal EU passport. Let's see what well be, if I am "only" going to be in transit...