Felix Mendelssohn’s Lutheranism is not in dispute.
Variation XIII from Elgar’s Enigma Variations was identified in its earliest sketch by a solitary capital L. Subsequent sketches include the extra letters ML to form the initials LML. Elgar scholars such as Byron Adams and Julian Rushton misinterpret these letters as a reference to Lady Mary Lygon, a noblewoman who graciously supported Elgar’s early musical career. At the same time the Enigma Variations were completed, Elgar dedicated his Three Characteristic Pieces to her, effectively ruling out Lady Lygon as the secret dedicatee. There is no reasonable explanation for Elgar to openly dedicate one work to Lady Lygon on the one hand, yet on the other conceal a second dedication unless it was for someone else. Patrick Turner sums up this dichotomy by observing the initials LML “...constitutes further evidence in favor of Lady Mary Lygon as the subject of this variation, but at the same time prompts curiosity as to why, if he used her initials at some point to identify the variation, did he decide to abandon them in favour of asterisks.”  Why indeed. Those close to Elgar knew Lady Lygon could not possibly be the hidden friend, for her friendship was no secret at all. These informed individuals included Ernest Newman and Wulstan Atkins, among others. They personally knew Elgar and knew better than to fall for an obvious ruse...unlike Adams and Rushton.
Since Lady Mary Lygon could not possibly be the secret dedicatee, what other conceivable explanation is there for Elgar to assign the initials LML to Variation XIII?
The answer is surprisingly simple yet elegant. In Variation XIII Elgar inserts four quotations from Felix Mendelssohn’s concert overture Calm Sea and Prosperous Voyage. Like Bach, Felix Mendelssohn was a devout Lutheran whose faith was expressed in numerous sacred orchestral and choral works. Consequently, the capital L may be viewed as the first letter in a name, one that identifies both the founder of Mendelssohn’s faith and the composer of the unstated Principal Theme to the ‘Enigma’ Variations: Luther. As I explain here, the unstated Principal Theme is Ein feste Burg, a famous hymn composed by Martin Luther, the father of Lutheranism. The addition of the letters ML to the original L may be reasonably interpreted as the initials for the composer of the covert theme. When Elgar assigned the initials LML to his later sketches of Variation XIII, he gave critical clues about the identity of the hidden theme and its composer. That he did so in stages, first with the capital L and latter appending the initials ML, helps set apart the initials for the composer of the covert theme from the faith he founded and Mendelssohn followed.
Why did Elgar quote the music of a devout Lutheran four times in Variation XIII? First, the unstated Principal Theme was composed by the founder of Lutheranism, and Mendelssohn was a convert to that faith. Second, the number four pinpoints the movement in which Mendelssohn quotes Ein feste Burg in his first extended symphonic work, the Reformation Symphony. In the fourth and final movement, Mendelssohn uses Luther’s Ein feste Burg as the basis for a series of symphonic variations. By quoting Mendelssohn’s music, Elgar cryptically implies by imitation that Mendelssohn quotes the unstated Principal Theme in a set of symphonic variations. Mendelssohn was Jewish by birth, a trait also shared by the secret dedicatee of Variation XIII. The Roman numerals overtly identify the initials for Elgar’s hidden friend (X = J, III = C).
Some may object to this line of reasoning on the grounds Elgar said Variation XIII “…refers to a friend who was crossing the ocean when the Variation was written.”  In a letter to August Jaeger dated May 2, 1899, Elgar wrote of Variation XIII, “The pretty Lady is on the sea & far away…”  In notes written in 1927 for a set of pianolo rolls of the Variations, Elgar’s original manuscript states, “The asterisks take the place of the name of Lady Mary Lygon.”  For the published notes it reads more generally, “The asterisks take the place of the name of a lady who was, at the time of the composition, on a sea voyage.” Despite these claims, it is well known that Lady Mary Lygon was not on a sea voyage when Elgar composed Variation XIII.  Is there some way to reconcile these seemingly incongruous comments from no less a source than the composer with the actual identity of the hidden friend?
There is a way, one that rather gracefully melds Elgar’s Roman Catholicism with the Lutheranism forming the melodic core of the Variations.
One of the many titles for Mary, the Virgin Mother of Jesus, is “Our Lady, Star of the Sea”. When Elgar belatedly acknowledged “Lady Mary Lygon” in 1927 as the secret dedicatee of Variation XIII, he all but named the mother of his secretive friend. As the special protector of those who travel the seas, Elgar’s “Lady Mary” was most certainly far away and “crossing” the sea when he composed that special movement.
In Variation XIII Elgar’s choice of keys for the Mendelssohn fragments (F minor, A flat major and E flat major) cryptically allude to a famous work for violin and piano, the F-A-E Sonata. This four movement piece is dedicated to Joseph Joachim, a renowned violinist who supported the music of Liszt and Wagner, and later championed Schumann and Brahms. The letters F.A.E. are an acronym for Joachim’s personal motto, Frei aber einsam (Free but lonely). During his youth, Elgar desperately wanted to become a famous violin soloist, something beyond his reach because he did not begin his formal instruction with Adolph Politzer until it was too late. Joachim was one of the most celebrated violin soloists of his generation, so Elgar's admiration for him is understandable.
Joachim's association with composers whom Elgar deeply admired, particularly Wagner and Schumann, surely intensified that fascination, especially since Joachim was a favorite of Queen Victoria and the British aristocracy. Elgar's deliberate pairing of Joachim's personal motto with Mendelssohn's music is deliberate as Joachim was a protégé of Mendelssohn. At the age of twelve Joachim performed Beethoven's violin concerto in London under the direction of Mendelssohn, and he remained a perennial favorite with the British nation for the duration of his career. It is remarkable that Joseph is the first name of the earthly father of Jesus, the husband of Mary. Elgar's overt references to Lady Mary Lygon and covert allusion Joseph Joachim solidify the identification of the hidden friend. To learn more about the secrets of the Enigma Variations, read my free eBook Elgar's Enigmas Exposed.
 Turner, Patrick. Elgar's 'Enigma' Variations - a Centenary Celebration. London: Thames Publishing, 1999, p. 74
 Ibid, p. 71
 Ibid, p. 69
 Ibid, p. 68.
 Ibid, p. 70