At LYS, stay airside—limited amenities but smooth flow, making exits not worth the risk.
Take the Rhonexpress to Part-Dieu (30 minutes, EUR 16.90). Take metro line D two stops to Bellecour, the central square. Walk 5 minutes south into Vieux Lyon. Spend an hour in the traboules (covered passageways, free to walk through with a guide map from the tourist office). Head back from Bellecour metro at the 2-hour mark.
Follow the Vieux Lyon route, then walk north 20 minutes to the Presqu'ile for lunch at a bouchon. Paul Bocuse's original Brasserie Le Nord at Rue Neuve 18 serves classic Lyonnaise dishes for EUR 20 to 35 per main. Walk back along the Saone riverbank. If time allows, take the funicular from Vieux Lyon up to the Basilique de Fourviere for views over the city (free funicular, free basilica).
With 10 hours, add the Musee des Confluences at the southern tip of the Presqu'ile (EUR 12, 2 hours). The building alone is worth the visit. Take metro line B south to Suchet, then bus 63. Or spend 2 hours on foot along both riverbanks.