I will be leaving on Swiss Air from LAX to Athens via Zurich with NO checked luggage. I land in Athens at 9:30pm, but I want to catch the RyanAir fight at 10:15pm flight to Rome. Is this enough time since I have my luggage with me or should I catch the 11:45pm flight?
No experience with this but it appears that Ryanair closes boarding 20 minutes prior to flight time. So if your flight gets in on time you have 25 minutes to deplane and find and get to the gate. Doesn’t sound too promising to me.
https://help.ryanair.com/hc/en-gb/articles/360017824898-Airport-Timeframes
Athens is a very large airport and even an hour is not sufficient time to count on making a transfer flight even in the best of circumstances. You have two legs in order to get to Athens. If either one is delayed, or if there is any labor action as there have been throughout a lot of European airports this summer, there’s a strong possibility you would not make your flight.
Non-EU/EEA Citizens
Irrespective of a passenger's visa requirements, all non EU/EEA citizens must have their travel documents checked and online boarding pass stamped at the Ryanair Visa/Document Check Desk before going through airport security. In addition all passengers departing from Moroccan airports must present their Boarding Pass at the local airport check-in facility.
From the link in the 1st response.
Having to go out and back through security to conform with the above pretty much ends any chance of success.
I estimate you have a 0.00000000000000000000000000000000000000001% chance of pulling it off.
Is there any particular reason why, from Zurich, you go to Athens for a few hours and then go to Rome, when there are Zurich-Rome flights with Swiss Air?
You will not make it. Apart from the non EU/EEA document check issue, Ryanair flights depart from the satellite terminal 15 minute walk from the main terminal.