Thanks for writing! To answer your questions: Purgatory is a Roman Catholic and Greek Orthodox doctrine of temporal punishment that is not shared by the major Protestant churches. The Roman church in particular, drawing on II Maccabees 12:39-45 and on some early traditions, has taught that Purgatory is "a place or condition of temporal punishment for those who, departing this life in God's grace, are, not entirely free from venial faults, or have not fully paid the satisfaction due to their transgressions" (from the online Catholic Encyclopedia). As the word "purgatory" suggests, it is a place where Christians are purged, or cleansed, of their shortcomings and sins, according to the Romanists.
Did CS Lewis believe in Purgatory? In his "Letters To Malcom: Chiefly on Prayer," chapter 20, paragraphs 7-10, Lewis indicates a belief in this intermediate state of cleansing. Lewis was one of Christianity's foremost apologists of the 20th century, and many of his writings -- as referenced on our Web site! -- are of tremendous encouragement and value to believers today.
But Lewis, by his own admission, was not a hermeneutical scholar; his forte' was apologetics (arguing for the philosophical validity of the Christian faith), NOT Bible interpretation. For example, as evidenced in his discussion of the imprecatory psalms in "Reflections on the Psalms," Lewis' interpretation of Scripture _sometimes_ left a great deal to be desired.
All of which brings us to your most-important question: why don't Presbyterians believe in Purgatory? Simple: because Scripture doesn't teach it! If you'll examine the Roman defense of Purgatory, you will find a barrage of references to humans' teachings (some early-Roman fathers) and a reference to II Maccabees. As a part of the Apocrypha, II Maccabees is not to be accepted as part of the canon of Scripture (God's inspired, and therefore perfect, Word, which is the church's ONLY authority in faith and practice; cf. II Tim 3:16-17).
In the end, it doesn't matter what Lewis or an early Roman bishop or an apocryphal, non-inspired text said. All that matters is what is contained clearly in the Word of God: the Scriptures of the Old and New Testaments. Far from offering any hint of Purgatory, Scripture teaches that ALL who believe on the Lord Jesus Christ for salvation are sanctified totally and perfectly by his once-for-all sacrifice (cf. Hebrews 10:10, I John 2:2a, Ephesians 1:1 and Paul's reference to the "saints" -- the "holy ones" -- in Ephesus, and Romans 8:28-30). Nothing is left to be done!
Scripture also teaches that "it is appointed to men once to die, but _after this (death)_ the judgment" (Hebrews 9:27), so there can be no time of cleansing after death. In that same vein, the Apostle Paul was confident that at the moment of his death, he immediately would go to be with the Lord in heaven (II Cor. 5:8).
Why not heed the teaching of God's Word and believe that THIS life, after one's conversion, is the time for Christians to put off the works of darkness and to grow in holiness? (See Colossians 3:5ff and Romans 12:1ff).