This is VERY pushing to the point of not being achievable it as TLV is concerned. heck, it's not possible in many major airports where security is not a nightmare.
Unless you hold an Israeli passport, make sure that LH knows you are connecting so they have security waiting for you at the transit area, or else you arrive and have to call them on a wall mounted phone - and it can easily take them 20 minutes to arrive.
Usually i would recommend doing immigration and going out to the check in area (LH Checkin is on arrivals level) however with one hour to go between arrival and departure check in desks will already be closed.
email TLV LH (email on lh.com) and advise them of your situation.
danny