Greetings. I am looking at a mileage ticket flying Lufthansa into Lyon, arriving at 2:00 p.m. How long would I need on the ground to collect baggage, clear immigration and customs and get to the train station to catch a train to Aix-en-Provence? I am aware that Marseille is the closer airport, but I'm trying to avoid the 5 hour and 40 minute layover in Frankfurt. Thank you.

There is insufficient info provided. Assuming following based on your another post:
1. You are flying from LAX
2. You are looking at LH1076 FRA-LYS arriving LYS at 14:00. It is usually a A319.

>>> How long would I need on the ground to collect baggage, clear immigration and customs and get to the train station to catch a train to Aix-en-Provence?
Immigration is irrelevant at LYS. You go through that in FRA. = 0 second at LYS
Customs. If you have nothing to declare, it totally depends on how fast you walk. ~2 seconds if you are a fast walker. A few minutes if you use a walker.
Your biggest uncertainty is your plane arrival. Then how quickly they have resources to offload the plane based on the actual plane arrival time. You can get some idea of the punctuality by looking at a site like https://flightaware.com/live/flight/DLH1076
The only part you have control is whether to check your luggage or travel only with a carry on. The A319 has large enough overhead bins for carry-on compliant luggage.
Also adding to the uncertainty is how you are getting to the Part-Dieu station. If you are using a train, I think the ticket machine only took coins or a CC where your U.S. CC card might not work. If you only have paper money, you can buy tickets onboard from a ticket inspector with a surcharge. https://www.lyonaeroports.com/en/access-transports/tram

Thanks greg. Exactly the kind of info I am looking for.

greg, to clarify, the TGV station at LYS is at Part-Dieu station, requiring a paid tram or train ride from the terminal to the station?