Yes and no. Theoretically, you can ask for anything. Jesus said, “Ask, and you shall receive.” He just didn’t say what you would get or when. It is useless to pray for anything that would be immoral or evil, since God will not give divine assistance so that we can sin, and it would be blasphemous to ask for anything sinful anyway.
Jesus shows the perfect attitude in petition prayer. Matthew 26:39 describes when Christ is in the Garden of Olives before His arrest, scourging, crucifixion, and death. During this time, called the “Agony in the Garden,” Jesus prays so intensely that He sweats drops of blood. The Scripture passage quotes Him as saying, “Father, if it is possible, let this cup pass, yet not as I will, but as You will.” That last part needs to be added to all our prayers. Catholic Christians are encouraged to pray for whatever they need but should always add the same proviso Jesus did, “yet not as I will, but as You will.”
Can you pray to win the lottery? God is not Monty Hall, and life is not Let’s Make a Deal. Praying to win at gambling, even if you promise to share your winnings or give them all to charity or to your church, is disrespectful to the Lord. Games of chance or sporting events should be amusement and nothing else. Praying that your favorite team wins the Super Bowl, the World Series, or the World Cup is not proper. God does not take sides in such things. Instead you should pray that everyone plays well, that no one gets hurt, that good sportsmanship is shown, and that the officials and referees are fair and just.
Who hasn’t prayed while taking a final exam or the SAT? There is nothing wrong with praying for a clear head and that you do your best, but prayer cannot and should not be used to replace study and homework. God gave us an intellect as well as a free will; He wants us to use both.