A Chatgpt enquiry on a good selection of restaurants to try in Lyon came up with a good variety.
A classic restaurant to try is La Mère Brazier(e). Book ahead for lunch or dinner. It is one of the bouchon lyonnais, Lyon's traditional restaurants, historically associated with hearty, rustic cooking. A particular type of meal to try is the La Meunière — a particularly good introduction to classic Lyonnais food. Expect things like quenelle de brochet, pâté en croûte and other traditional dishes.
For modern Lyonnais cooking try Brutal, a contemporary néobistrot in Ainay. It's a good way to experience where Lyon's food scene is going rather than simply eating historical Lyonnais dishes.
For something a little more accessible [i.e., cheaper, I assume], Le Cochon qui Boit, Cinq Mains(e), Agastache and M Restaurant are among the city's current Micheli Bib Gourmand selections. This is the category I'd [i.e., Chatgpt's] particularly explore if you have several nights in Lyon: seasonal French cooking, good wine and less formality than a starred tasting-menu restaurant.
e = has English on its website