TGV Lyria is a crappy ripoff company. book the reservation only till the last stop within france and take regional trains from there.
On the link above it is told to go via Lyon but actually the best and fastest route is via Bellegarde.
- TGV Paris - Bellegarde 10€ limited fare, then 20€
- TER Bellegarde - Geneva
- any train to Lausanne
Not that much longer than the direct train. If you'd like advice let us know your travel date.
Check availability and price here for domestic TGVs : https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish
4€ booking fee per order compared to 2€ per person per train on eurail.com
TGV Lyria has indeed the most expensive seat reservations costs but there are ways to avoid them. :)