Frankfurt layover

This is a few years old, but might be a useful option:

"Frankfurt on the fly: A long layover allows for a walking tour of the German city"
https://wapo.st/3J84GAu

Definitely contact Frankfurt on Foot. I booked a private tour last fall for our group of four when we had one night in Frankfurt, and was very happy with our guide! The website describes the "Layover Tour". I had emailed with a few questions and received prompt replies. I found it helped us make the most of our limited time in Frankfurt.

I am sure Ms. Jo will chime in with most of your questions, but as someone who recently went to Frankfurt, I can tell you that spending a few hours in Frankfurt will be worth whatever trouble you have to go through to sort out your left luggage. I loved the city and I am sure you will consider it time well spent. The train station is hooked onto the airport so it is so easy to get into town and back.

if our luggage is checked through to Athens, we won’t have to claim it
and recheck it, correct?

I believe that is correct, however, just in case the airline returns your luggage for layovers more than a certain time, check with you airline to be sure. Make sure the luggage tag says 'Athens" (ATH). I've heard that some airlines, for extended layovers, send the luggage to baggage retrieval, and you have to recheck it before continuing, but I don't think this will happen in your case.

are there lockers for this? Where?

I don't know. Never needed them. Maybe Jo can tell you.

is the train the best way to get to city center.

Yes. The S-Bahn to Frankfurt leaves from the Regional Bhf, which is under the transit building on the other side of the access road from Terminal 1. You don't have to cross the road, there are escalators just inside the outer wall of Terminal 1 that go to the passageway that goes under the street to the Bahnhof.

By the way, our own Ms Jo leads a Frankfurt tour, Frankfurt on Foot.

On the way back to the airport, we just have to get through security

Correct. When you arrive in Frankfurt, before you get out of the transit zone of the airport, in order to enter Germany, a Schengen country, you will go through immigration (passport control). When you leave for Greece, another Schengen country, you will not need to go through passport control again. That's the whole idea of Schengen.

No lockers in airports. Think of the security.
They have luggage storage facilities that are very secure. Cost is 9.50€ for the day, per piece of luggage. Alternative is to get off the train at the main station and toss your bags in a locker there that costs 5€. Should be able to get a few bags in each locker if they are soft bags.