The Silk Roads by Peter Frankopan (2015) is not about Lyon specifically, but Lyonnais silk merchants were among the key actors in the global trade networks it describes. It gives context for why Lyon became one of Europe's great cities.
Traboules de Lyon by Édouard Herriot (various editions) — the former mayor of Lyon and long-serving politician wrote about the city's hidden passageways with characteristic Lyonnais civic pride. French only, but worth hunting down.
Monsieur Hire by Georges Simenon (1933) — not set in Lyon, but Simenon lived in the city for a period and his methodical, atmosphere-heavy procedurals echo the city's reputation for quiet, competent seriousness. His Maigret novels are the best companions for slow eating and slow walking in any French city.
Tender is the Night by F. Scott Fitzgerald (1934) — the Riviera-set novel has scenes in Lyon, which in the 1920s was still on the main road south from Paris. The Grande Corniche journey Fitzgerald describes passes through what is now the autoroute du soleil, but the eating and drinking stops were in Lyon.