If you wish to learn more about the biblical approach to fasting and prayer, John Piper has written an incredible book on the subject, A Hunger for God: Desiring God Through Fasting and Prayer, in which he "invites you to turn from materialism and sharpen your appetite for God through prayer and fasting. [Piper's] exploration of fasting will help you understand how this ancient biblical practice can nourish your spiritual life and satisfy your longings."
As with many holidays in the liturgical calendar of Christian orthodoxy, a Christian is certainly free to observe Lent if he or she chooses to do so. "The key is to focus on repenting of sin and consecrating oneself to God," Got Questions concludes:
"Lent should not be a time of boasting of one’s sacrifice or trying to earn God's favor or increasing His love. God’s love for us could not be any greater than it already is."