How will you arrive into Lyon?
If by plane, the main airport is far outside town and you wouldn't need to drive into town to go north to Bourgogne, so I would rent there.
If by train, I would ask what kind of car you intend to rent. If a manual transmission, and if you're intimidated by driving in Lyon, then take the train up to Dijon and rent there if it would make you feel better.
On the other hand, if you need an automatic, you're better off renting in Lyon. It's a much bigger city with a much bigger rental pool.
Driving in Lyon isn't terrible. It's just irritating. Lots of tailgating. If driving through the central city prepare to be blocked by trucks making deliveries on one-way single lane streets. Prepare for traffic jams on the highways leaving the city, especially this time of year.
It's a hassle but it's not insurmountable for the average experienced American driver.