how can I travel from Lyon to Conque by train or bus?
I assume you mean Conques-sur-Orbiel near Carcassonne.
If so, Carcassonne is the nearest railway station, some 6 miles/10km distant.
Lyon Part-Dieu to Carcassonne is about a 4 hour train journey, a couple of direct trains but otherwise change at Montpellier. Train times, fares and reservations (essential) at www.voyages-sncf.com
There is bus between Carcassonne and Conques-sur-Orbiel, route 43, which leaves from the Boulevard Varsovie, a little walk from the station. So far as I can tell there are three buses a day at 1200, 1215 and 1715, none at all at weekends. Details at http://audelignes.cg11.fr/
I hope that helps.