Train from Lourdes to Bayonne, and then to St-Jean-Pied-de-Port, or a taxi. I doubt you could drop off a hire car at St-Jean - it is only a small place. Taxi fares in France look as if they vary from about 1 euro 20 (Paris) to 1 euro 80 (Nice), plus a flag fall of a few euros. The cost would depend on the route taken - main road through Pau and Orthez would be faster but further (about 150km), or small secondary roads cross country to Marie Ste Oloron and from there to St-Jean. Have a look at a map.
We once took a taxi from Pau to get dropped back on the Le Puy route (after sending husbands home), and we negotiated a price with the taxi driver at the train station.
