I'm not sure you can visit the underground lake:
http://www.paris-tourism.com/paris/us/patrimoine_loisirs/monuments/garnier_opera___national_opera_of_paris.htmlMore info in English:
http://visites.opera-de-paris.com/?theatre=garnier&page=visiter&lng=enI actually work like 5 minutes from the Op?ra.
As for Paris - Lourdes, you can take the train with the national train company SNCF:
http://www.voyages-sncf.com (I'm not sure they have an English version)
Around mid-April, a roundtrip would cost 44 euros ($56): 07h45 22.00 ? / Length: 05h59 - 17h05 22.00 ? / Length: 06h15. That'd be a long trip (12 hours round trip!) just to go there, maybe you could stay overnight.
Don't hesitate to ask or PM me if you need more info.