Aha, it's working! :)
To use your own line of reasoning (we want God to listen to us) the saint is praying for something "HE" wants when he prays for others. If the other is a lost person, then that person does not want the object of the prayer, leaving only the saint to have his prayer answered.
It's not wanting as in "I pray, you give" but asking. The intent is different. The saint is perfectly content that the final result, whether his prayers are fulfilled or not, is a merciful and just decision. He does not place a condition of expectation, but leaves everything to God, realizing that his own prayers may be unworthy.
If the other is a lost person, then that person does not want the object of the prayer, leaving only the saint to have his prayer answered.
You also don't know if the lost person does not want or doesn't know how to ask for God's help. Most people who are lost simply don't know how to pray. That doesn't mean they don't want to pray.
FWIW, meant to ping you to 15809. Sorry.