Reviewing Pænitemini, the 1966 law of Pope Paul VI amending and regulating the age-old norms of penance for Lent, I came across a few points of possible interest to you my readers. The numbering is my own.
1. Penitence is of divine precept: "By divine law all the faithful are required to do penance."
2. "The [entire] time of Lent preserves its penitential character..."
3. "The precept of penitence must be satisfied in a more perfect way by priests, who are more closely linked to Christ through sacred character, as well as by those who in order to follow more closely the abnegation of the Lord and to find an easier and more efficacious path to the perfection of charity practice the evangelical counsels."
4. All the laity are invited to do corporal mortification. "The Church,... invites all Christians without distinction to respond to the divine precept of penitence by some voluntary act, apart from the renunciation imposed by the burdens of everyday life."
5. Rich countries should do greater penance. "...[W]here economic well-being is greater, so much more will the witness of asceticism have to be given in order that the sons of the Church may not be involved in the spirit of the 'world,' and at the same time the witness of charity will have to be given to the brethren who suffer poverty and hunger beyond any barrier of nation or continent."
6. The custom of abstinence from meat and fasting throughout Lent should be preserved where possible. "...[T]he Church, while preserving--where it can be more readily observed--the custom (observed for many centuries with canonical norms) of practicing penitence also through abstinence from meat and fasting, intends to ratify with its prescriptions other forms of penitence as well..."
All of this is consistent with my previous posts on this matter of the Lenten penitential practice of the Church.
God requires us all to do penance and the Church acknowledges that and still strongly encourages the traditional way, though the old norm is no longer binding under pain of sin.
For further study on this matter I suggest you read the entire document which is very instructive regarding God's will of men doing penitence. Footnote 53 of Pænitemini has an excellent bibliography from the New Testament and the Fathers of the Church on the matter of the necessity of fasting and corporal penance.
"53. A) In the New Testament: 1) words and example of Christ: Matt. 17:20 (cf. Mark 9:28); Matt. 5:29-30; 11:21-24; 3:4; 11:7-11; and 4:2; Mark 1:13; Luke 4:12; cf. Matt. 8:18-22; 2) witness and doctrine of St. Paul: 1 Cor. 9:24-27; Gal. 5:16; 2 Cor. 6:5; ibid. 11:27; 3) In the Early Church: Acts 13:3; ibid. 14:22; etc.
"B) Among the Fathers: several references arranged according to order of time: Didache 1:4 (F. X. Funk, Patres Apostolici, ed. 2, Tubingen, 1901, 1: 2); Clement of Rome; 1 Cor. 7:4 and 8:5 (Funk 1:108-110); 2 Clement 16:4 (Funk 2:204); ibid. 8:1-3 (Funk 1:192- 194); Aristides, Apologia 15:9 (Goodspeed, Goettingen, 1914, 21); Hermas, Pastor, Sim. 5:1, 3-5 (Funk 1:530); cf. ibid. Sim. 7:2-5 (Funk 1:554); Tertullian, De Paenitentia 9 (ML 1:1243-1244); Tertullian, De Jejunio 17 (ML 2:978), Origen, Homeliae in Lev, Hom. 10:2 (MG 12:528); St. Athanasius, De Virginitate, 6 (MG 28:257); ibid., 7, 8 (MG 28:260, 261); Basil, Homeliae, Hom. 2:5 (MG 31:192); Ambrose, De Virginitate, 3:2, 5 (ML 16:221); idem, De Elia et Jejunio 2:2, 3:4, 8:22 and 10:33 (ML 14:698, 708); Jerome, Epistola 22:17 (ML 22:404); idem, Epistola 130:10 (ML 22: 1115); Augustine, Sermo 208:2 (ML 38:1045; idem, Epistola 211:8 (ML 33:960); Cassian, Collationes 21:13, 14, 17 (ML 49:1187); Nilus, De Octo Spiritibus Malitiae 1 (MG 79:1145); Diadochus Photicensis, Capita Centum de Perfectione Spirituali 47 (MG 65:1182); Leo the Great, Sermo 12:4 (ML 54:171); idem, Sermo 86:1 (ML 54:437-438); Leonine Sacramentary, Preface for Autumn (ML 55:112)."
Cf. Here is a blog which systematically sets out all of the present relevant legislation on the matter.
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