Does fasting actually help with lust?

Yes. In the Orthodox Church we fast following the church calendar, and several things happen when we do. First, we are being obedient to what has been handed on to us by our holy fathers. One of the earliest documents we have, the Didache, says the Lord prescribed fasting on Wednesdays and Fridays: Wednesday because he was betrayed, Friday because he was crucified.

Christ himself said, when I am here they will not fast, but after I am gone, they will fast. If we only fast when we feel like it, we're just doing our own will, and there's no obedience in that. The prescribed fast is predominantly vegan, no animal products, and the holy fathers tell us this fast calms the temptations and desires of the body. We are psychosomatic beings: soul and body work together.

During the 40-day fasts before the Nativity and before Pascha, life slows down and becomes more conducive to prayer. Also, when we fast in obedience, we show humility, and this humility attracts the Holy Spirit. When the Holy Spirit sees us striving to calm our passions, he gives us additional help. Without God's help we will not overcome this. I use the analogy of the bench press: we push with all our might, but sometimes the weight is too heavy, and God grabs the bar and gives us a nudge, so his strength and ours together overcome the temptation.