Lyon-Paris:

https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish

Paris-London:

https://www.b-europe.com/EN/Booking/Pass#TravelWish

Thanks for your answer.

It works for the Paris-London but doesn’t for the Lyon Paris. I’ve tried with many different dates without success.

Works for me:

Be sure to choose "Paris (fr)” and not a particular station in Paris.

If it still doesn't work for you, then what date do you want to travel?

Btw if you'd like to avoid the station transfer in Paris : there are a few direct TGVs to Lille-Europe. From there you can board Eurostar trains to London (they often have more availability than from Paris).