How can I get from Dieu Station to Perrache Perrache Station when I arrive and then back to Dieu when I leave? I think I can hop a TGV Train between stations, but doesn't that require a reservation? What about a bus/metro/tram?
Get the tram. You can do it by metro, but it needs at least one change of line with carrying suitcases up and down stairs. The tram is direct and it's mostly protected from road traffic delays. NB: It's Part-Dieu, not just Dieu. Most European people rarely abbreviate street and place names the way Americans do.