He became a Benedictine in Melk Abbey, 10 September 1654. At the order of his abbot, he applied himself to the study of law at the University of Salzburg, where theological studies were committed to the care of the Benedictines.
He was proclaimed doctor of civil and canon law in 1657, ordained priest in the following year, and was soon professor of canon law at this university.
In 1669 he was unanimously chosen vice-chancellor of the university. He left Salzburg in 1674 at the invitation of the Abbot of Melk, who hoped that Engel should become known and appreciated by the monks, to be chosen as his successor. The death of Engel, which occurred in the same year, prevented this plan from being realized.
His main works are:
- "Manuale parochorum" (Salzburg, 1661);
- "Forum competens" (Salzburg, 1663);
- "Tractatus de privilegiis et juribus monasteriorum" (Salzburg, 1664);
- "Collegium universi juris canonici", etc. (Salzburg, 1671–1674), a work running to a fifteenth edition in 1770. A summary was published in 1720 by Mainardus Schwartz.
- Herbermann, Charles, ed. (1913). "Ludwig Engel". Catholic Encyclopedia. New York: Robert Appleton Company.
- Ziegelbauer, Historia litteraria ordinis Sancti Benedicti. (Augsburg, 1754), III, 401, IV, pp 231, 238, 593.
- Schulte, Geschichte der Quellen und Literatur des canonischen Rechts. (Stuttgart, 1875–80), III, p 150.
- Eberl in Kirchenlexikon, s. v.
- Keiblinger. Geschichte Von Melk (1867), I, p 899.