Orientation: Sarria is located on a road that goes from Monforte de Lemos to Lugo. There is Renfe train that goes from A Coruña to Monforte de Lemos and points beyond.
The closest airport is Santiago Labacolla SCQ. Other airports of interest due to transportation services would be A Coruña and Vigo.
I note that Lourdes Tarbes Airport has no regular destinations in Spain.
Otherwise ...
SNCF train from Lourdes to Irun/Hendaye.
Metro Donostialdea from Hendaia (co-located gare d'Hendaye) to Irun Colon (across tracks from Renfe station)
You will likely require an overnight stay at Irun.
Renfe train from Irun Renfe Station to Sarria.
If you fly to Madrid take Renfe train from Madrid to Sarria.
If you fly to Santiago take Empresa Freire bus from Labacolla Airport to Lugo and Empresa Monforte bus (Monbus) from Lugo to Sarria.
If you fly to A Coruña take Arriva bus from bus station to Lugo and Empresa Monforte (Monbus) bus from Lugo to Sarria
If you fly to Vigo take Renfe train to Monforte de Lemos and Monforte de Lemos to Sarria. Empresa Monforte (Monbus) operates buses from Monforte de Lemos to Sarria if the train connection doesn't work well.
If you fly to Santander or Leon ... you can take ALSA bus to Lugo or Renfe train to Sarria via various transfers.
Links of interest
Concello de Sarria Transporte
http://sarria.es/index.php?option=com_content&view=article&id=109:transportes-y-horarios&catid=60:localizacion&Itemid=132&lang=gl
SNCF
http://www.sncf.com/en/passengers
Renfe
http://www.renfe.com/EN/viajeros/
Aena Santiago (you can get the other airport sites here too)
http://www.aena.es/csee/Satellite/Aeropuerto-Santiago/es/
Empresa Freire
http://www.empresafreire.com/
Monbus
http://www.monbus.es/en
Arriva
http://www.arriva.es/en/