Does God, according to Catholic theology, precondition His help on other people's prayers and if so, why? We are told by the Church many times the importance of prayers for others. It would seem that we can help other people by praying for them, or, to be more precise, we can plead God's grace for those who we pray for.

Let us reverse this statement. Then it would seem that if we don't pray for others, then God will deny them His grace He would give them if we were praying for them.

This seems to be almost explicitly stated in Fatima apparitions:


  Pray much and make sacrifices for sinners, for many souls go to hell because there is no one to make sacrifices for them.


Does this mean that God preconditions His aid for sinners on other people's prayers? If so, why? How to reconcile such a statement with God's infinite love, according to which He should do whatever is possible and whatever will not violate a man's freedom to save them from eternal damnation and bring them to Heaven? Since the fact that no one prays for a man is hardly their guilt, how to reconcile such a statement with God's fairness, according to which he probably shouldn't precondition His actions towards a person on anything other than that person's will, and especially not if eternal salvation is at stake?
First, you must understand what the RCC teach about grace. Here.
2002

God's free initiative demands man's free response, for God has created
man in his image by conferring on him, along with freedom, the power
to know him and love him. The soul only enters freely into the
communion of love. God immediately touches and directly moves the
heart of man...

Following this quote, if a person never responses he might need help from other's prayer. Through the other's intercessions, God can grant him many other opportunities where he can response. God will not violate man's free will and won't force him to response. If a man won't response God can't immediately touches and directly moves the heart of man.
You are saying

Does this mean that God preconditions His aid for sinners on other
people's prayers?

Yes and no. First of all, God gives enough and sufficient opportunities to every man for his conversation. If a person runs out and fails to answer God's calling then other's prayers and sacrifices can bring more and new opportunities.