Marlowe, while he was still at the University of Cambridge, translated works by the Classical Roman poets Ovid and Lucan. The scholarly reading and translation of ancient Latin (and sometimes Greek) was required of all students in all disciplines at Cambridge at this time. It was not only a school subject to read and translate the Classics, but it was also a fashionable pursuit.
Ovid (Publius Ovidius Naso) first published his Elegies (also known as Amores) in 20 BC. The second edition, consisting of a reduction of the original five books to three, was published in 1 BC. This second version is the one that Marlowe translated. It was the only version available, as the first is lost to history.
The word "elegy" is misleading in its modern English sense in the case of Ovid's work. The Latin word elegia meant simply any poem written in a certain kind of meter. "Any poem written in elegiacs (also called elegiac couplets,) that is, in alternate lines of hexameter and pentameter" (Howatson 208). "Elegy" did not mean a poem written specifically about a person who has died, as the word has come to mean in English. During Ovid's time, elegies were poems that expressed personal sentiments (including love poems, epitaphs, and laments) -- as separate from narratives, which would usually be termed "epics". The distinction from "lyric" poetry cannot be taken the same way it is represented in English. During Ovid's time, the term "lyric" was mostly a musical distinction.
The Roman Amores might originally have been published under the name of the main female character -- one hesitates to call her a heroine -- Corinna. Though this woman is drawn with humanity and idiosyncracies, it is doubtful that any Corinna, or a woman like her in Ovid's aquaintance, ever existed (Howatson 401). The poetic "mistress" of Latin elegia was merely a device, much as the "lady-love" of which the medieval troubadours sang was not necessarily representative of any real person. The form of Ovid's poem is stylized and part of a tradition of love poetry which was concerned more with style, wit, and poetic invention than it was a chronicle of particular lovers' emotions, or the personal feelings of the poet.