You can go to the TLV gate quite easily without entering Schengen. There is a quick and easy security check and then you can turn sort-of rightwards to continue to the Non Schengen area where there are a small number of food and drink options but no showers. There are 2 cafés, I think, there are vending machines and one of the shops has water and snacks. Not a lot but there is something. Instead of turning right you could go left and join the queue to enter Schengen. Now the border guards aren't over-enthused at people going into Schengen purely to visit a lounge, from their perspective it's adding unnecessary work for them when there are sometimes long queues, but if you have plenty of time they will allow this, particularly if queues aren't so long. There's the TAP and ANA lounges, the latter is allowing shower access for an extra fee. TAP isn't yet allowing showers. Plust lots of shops and restaurants.

The extra checks for TLV are probably less than for the USA at the moment, and don't add more than a few minutes to the process. However they do open the gate and boarding sooner than for short haul services.