Is public transportation available in Lyon at night? If yes, until what time does night transport run?
According to Wikivoyage
Metros and trams run approximately from 5AM to midnight. Some bus lines do not run after 9PM. Check the TCL website for details :
Detailed schedules [French link replaced with English version, thanks to @audionuma]
There you will also find 4 night bus lines ("lignes pleine nuit" / "full moon lines") that run Thursday to Saturday night every hour.
Alternatively Lyon also has a functional rental bicycle system called "Vélo'v" (like "Velib" in Paris) that you could use for your trip home at night. For more info refer to Wikivoyage once more.