I don't often read the Daily Mail, apart from the puzzle page; however, a few days back I spotted an interesting reader's letter from a correspondent who recalled having been taught, in his very traditional Scottish school, a misspelling of "dilemma" as "dilemna".
No doubt of it: "dilemma" - etymologically from Greek δί-λημμα ("double proposition") - is correct, and the Oxford English Dictionary - quoted at the discussion at Wordwizard - confirms this. But a look on the Web finds many other people with a distinct recollection of having been taught otherwise.
I believe them, because this seems more than just an occasional misspelling: on Google Books "dilemna" gets 8,870 hits to 2,333,000 for "dilemma" (i.e it accounts for about 0.4% of occurrences in published books), and Google Ngram Viewer finds it to be long-standing (British English / American English). It's not limited to low-quality publications; examples include scholarly texts (e.g. here and here); Punch magazine (here); the works of William Pitt (here); the works of Washington Irving (here); and English classics such as Fielding's Amelia (here), Defoe's Robinson Crusoe (here), Swift's Gullliver's Travels (here) and Smollett's The Adventures of Sir Launcelot Greaves (here). It's hard in particular to believe that the last batch of writers, and their proofreaders, would all make the same spelling mistake, so I can only conclude "dilemna" to be a genuine variant spelling that has been propagating, undocumented,.for centuries.
dilemna / dilemma), which is the same period, according the the OED, when "dilemma" itself entered English. I rather wonder if it originated as a misreading from Gothic script. In some of its forms, as in the above example from Medieval Writing and Scripts, words tended to consist of horizontally-condensed and very similar verticals: "mm" and "mn" wouldn't look much different.
Alternatively, maybe the error crept across from mathematics teaching. Euclid's Elements in Latin was a standard text that persisted long after Henry Billingsley's first English edition came out in 1570. The Dutch-printed 1692 edition by Henrik Coets spells "lemma" - a mathematical proposition - as "lemna" (examples).
(There is, by the way, a Greek word "lemna" - but it's duckweed).