Of course, you can buy your ticket in Lyon at the Lyon Part Dieu station...
Looking at the SNCF site and your arrival time on August 25, there is only one train for you. It leaves Lyon Part Dieu station at 17.06 and arrives in Le Puy at 19.17. The Rhone Express will stop at Lyon Part Dieu. So you will have two hours to deplane, go through French immigration and customs, walk to the Rhone Express station, and take the Rh. Expr. into Lyon.
I purchased my tickets online and directly from SNCF until my last trip. Then my U.S. credit card would not work. Through comments on this board I became aware of Capitaine Train and used them to buy my ticket (and my wife's) last May. With Capitaine Train you just print your ticket on your home printer and present it to the conductor. Capitaine Train will answer your question about the ticket's validity for a future train (in case you are delayed). They respond to questions in English and, based on my experience, do so promptly. I recommend you query them and you can also ask whether a seat on the 17.06 train can be reserved (I don't think there are reserved seats on this train).
Bon chemin.