How do people benefit from Lourdes?

The benefits of going to Lourdes are the same for any site we believe to be a supernatural location. The key to the benefits is not the location but your intent. God knows your intent. If it is to getting bragging rights to your friends you will get the opposite. If you are reaching with full sincerity to God asking for healing you will get that. It is not based on the location but on the expectations of your heart, not even Jesus could heal someone that didn't expect it. What you expect / pray /ask of God is what you will get buffered by God's kindness.