What is the foundational motivation of Lenten practices? Lent is traditionally described as lasting for 40 days, in commemoration of the 40 days Jesus spent fasting in the desert, according to the Gospels of Matthew, Mark and Luke, before beginning his public ministry, during which he endured temptation by Satan. - Wikipedia


I included this Wikipedia quote only because it was easiest and really seems to reflect a near universal consensus on the symbolic purpose of the Lenten season.  Various traditions practice Lent differently and some do not practice at all but the underlying Scriptural basis appears to be agreed upon among those who do.

The three synoptic gospels use 3 different words which carry different degrees of intensity to describe Jesus departing into the wilderness by the Holy Spirit:


  Mat 4:1  Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil.
  
  Mar 1:12  The Spirit immediately drove him out into the wilderness.
  
  Luk 4:1  And Jesus, full of the Holy Spirit, returned from the Jordan
  and was led by the Spirit in the wilderness


Two things immediately jump out:  First, Jesus did not go into the wilderness of His own accord but was taken there (led or driven) by the Holy Spirit and, second, He was taken there for the purpose of being tempted (more accurately tested) by the devil.

Since there is unanimity in the Scriptural basis of the practice but differences in the application of the practice I am wondering if there is unanimity in the spiritual, motivational desire.

Are Lenten practitioners attempting to enter into Jesus' experience of having been led or driven by the Holy Spirit into deprivation to be tested by the devil or is it more of a ritual of remembrance?
What are the fundamental motivations of the "Lenten Practices"?

Not all denominations observe Lent! There are a few fundamental motivations for partaking in the Lenten observation.


Preparation spiritually for celebrating the sacred paschal mysteries of Christ’s Passion, Death and Resurrection.
Imitating Our Lord Jesus Christ who gave us the example of how to fast during his temptation in the desert.
It is a time for spiritual renewal, through prayer, fasting, almsgiving and other forms of Lenten practice.


No doubt the most Christians will be in accord with the fact that Lent is a time for preparing ourselves for the great contemplation for paschal mysteries which will be celebrated during Holy Week and Easter Sunday!


  Lent is a solemn religious observance in the Christian liturgical calendar that begins on Ash Wednesday and ends approximately six weeks later, before Easter Sunday. The purpose of Lent is the preparation of the believer for Easter through prayer, doing penance, mortifying the flesh, repentance of sins, almsgiving, and self-denial. This event is observed in the Anglican, Eastern Orthodox, Lutheran, Methodist, Moravian, Presbyterian, Oriental Orthodox, Reformed, and Roman Catholic Churches. Some Anabaptist and evangelical churches also observe the Lenten season. Lent (Wikipedia)    


Although some denominations do not fast, many do such as Catholics, Eastern Orthodox, Lutherans and so on. The traditional ways to prepare for Easter is through prayer, fasting and almsgiving. 


  Prayer: Without prayer, fasting and almsgiving are merely actions we do out of tradition without much meaning. Prayer is our conversation with God. It is through prayer that we find the strength to fast. It is through prayer that we develop a closer, more intimate relationship with God. This relationship makes us so grateful for the blessings he has bestowed upon us, that we eagerly give to those less fortunate than us. The Church, in its wisdom, understands that prayer is essential to any action we Christians may undertake.
  
  Fasting: Fasting is one of the most ancient actions linked to Lent. Fasting rules have changed through the ages, but throughout Church history fasting has been considered sacred. The prophet Isaiah insists that fasting without changing our behavior is not pleasing to God. Therefore, the goal of fasting is linked with prayer. The pangs of hunger remind us of our hunger for God, and prayer and fasting together brings us to what Lent is about - a deeper conversion.
  
  Almsgiving: It should be obvious by now, that almsgiving is simply a response by us to God, a response that we have come to through prayer and fasting. It is an expression of our gratitude for all that God has given us, and a realization that in the Body of Christ, it is never just "me and God." Through prayer and fasting we come to a deeper understanding that the needs of all are the responsibility of all in the Body of Christ. Works of charity and the promotion of justice are integral elements of the Christian way of life we began when we were baptized.
  
  Why are prayer, fasting and almsgiving especially important during Lent?


It should be noted that Lent is not universally observed throughout Christendom.


  In the Anglican churches The Book of Common Prayer prescribes that Lent be observed with fasting. In Lutheran and many other Protestant churches Lent is observed with various services and practices, though Lent is not formally observed in many Evangelical or nondenominational churches. - Lent (Encyclopaedia Britannica)


Christians who strengthen their faith with the three traditional practices of prayer, fasting and almsgiving are truly preparing themselves for the great events of Christ’s Resurrection on Easter Sunday. These are not the only practices Christians do during Lent. 

More information may be gleaned from the following articles:


How Prayer, Fasting, and Almsgiving Help Fight Temptation
12 Traditional Catholic Lenten Practices
Lent: A Rookie Anglican Guide
Lutheran Liturgical Practices During Lent