One hour is definitely a extremely tight connex for the TLV flight due to longer security procedures. As security for the TLV flights is largely managed/supervised by staff from Israel, it is their call wether they will take you or not. If you are in F LH might give you a direct limo transfer, however even in this case the non LH security staff might give a thumbs down.
If I were you I would work on an alternative through VIE,IST or ZRH before departure.