There is no direct connection from Lyon to Oingt. However, you can take the train to Villefranche-s-Saone then take the taxi to Oingt. Alternatively, you can travel from Lyon to Oingt in around 35 min.
How to get from Lyon to Oingt
From Lyon Part Dieu train to Villefranche-s-Saone then taxi to Oingt. 40 min 37€. From Lyon taxi to Oingt. 35 min 55€. From Lyon drive to Oingt. 35 min 4€. From Lyon Uber to Oingt. 35 min 67€.