Maybe I can add some clarification to this "no licence" story. A couple of things got a bit mixed up here:

A licence basically is what gives pilots the permission to transport passengers for money. There are variants, but any commercial airline pilot has a licence. So does every LX pilot.

Then there is the rating. The rating is given for one or several types of aircraft. It is obtained after training on that aircraft type (in sim and in flight). To keep the rating for a particular aircraft type, a pilot has to fly on that type every so often. I believe for LX pilots flying Airbus, they have to fly every 3 months to keep their rating.

So, the issue at hand in TLV was not an issue of the pilot not having a licence (that would be scandalous), but not having the proper rating for the aircraft to be flown.

Now some may same "but how can that happen?". Very easy: LX has three groups of pilots. Those that only operate the A32S fleet (A319-A320-A321), those that fly A32S and A330, and those that fly A330 and A340. The typical career is to start on the A32S type, then get trained on the A330 and thus be in the A32S+A330 group, then be trained on the A340 and be in the A330+A340 group. So, what probably has happened is that the co-pilot was a member of the A330/A340 group. So he could very well have flown the A340 plane from ZRH to TLV the previous day. As a member of the A330+A340 group, he probably hasn't flown an A32S type for more than 3 months - so he has lost his rating for the A321. So he can't fly the A321 back to ZRH.

"But then why does this problem only occur for the co-pilot, the pilot must have had the same problem"? Not necessarily. It may be the case that the pilot just got his A340 training, so his membership in the A330+A340 group is relatively recent. Which means that his last flight on an A32S is less than three months in the past, which means he still has the rating for an A321.

Another possible explanation is that the previous day the flight was operated by A330 and not by A340. Which means the crew could come either from the A32S+A330 group or the A330+A340 group. So if the pilot came from the A32S+A330 group, he would have the rating for both the A330 (for the ZRH-TLV flight) and the A321 (for next day's A321 flight back). The co-pilot may have belonged to the A330+A340 group - not a problem from the outset, because he was supposed to fly back on an A330 the next day. But then LX switched to an A321, and he couldn't fly that plane anymore because he only has the rating for the A330+A340.

Maybe there's another explanation, but these seem plausible. I guess they were just unlucky in the rostering of the cockpit crew or deployment of plane.

And by the way, the crew does stay in TLV over night.