Train from Lyon to Paris

If you want discounted nonrefundable tickets, buy them now. They are now mostly going for 45 EUR on May 15, and late trains as low as 25 EUR. Prices will only go up as time goes by, until they get to full price, 105 EUR.

Tickets are available now, and the cheapest ones are already being snapped up by other people. The cost will likely increase a lot as you wait. Check out the fares for your anticipated travel date on the SNCF website now. The cheapest options will be non-refundable/non-changeable, so you must be sure of your travel date before purchasing.

I just looked at fares for May 16 (randomly-chosen date). It appears the full (walk-up) fare is 105 euros. There are non-exchangeable ticket still available for some trains, priced at 45 euros. But those will not last forever.

The Lyon Part Dieu station is large and can get extremely busy, to the degree that it can take you a few extra minutes just to weave through the crowds to reach your platform, so don't cut it too close on departure day.

I am seeing ouigo tickets for May 16 as cheap as 16 EU.

(Ouigo is a budget program from SNCF, the national railway.)

Those Ouigo trains go from St Exupery Airport, so you will have to get there to take them.