Thank you both for the advice!

NWIFlyer, are you saying that they will allow our checked luggage into the lounge?

We were planning on returning around 7pm to be able to rest a bit before our flight. By the time we land at Athens at 9:15am, it will have been 18 hours since our first flight the previous morning, not counting the hour's drive to the airport + check-in process. With an 11:50pm departure, we won't arrive in TLV until 1:50am and then will drive to our hotel after that. Thankfully, the flight to ATH is nearly 10 hours in business, so we should be able to rest on that leg. But I'd imagine we'll be a bit tired by the evening after such a long layover. Perhaps we'll stay out a little longer and enjoy more time in Athens.

I'm familiar with the public transportation in Athens. Would you recommend the bus or the metro into the city?

Thanks again! So appreciate the feedback.