O.E. lust "desire, pleasure," from P.Gmc. *lustuz (cf. O.S., O.Fris., Du., Ger. lust, O.N. lyst, Goth. lustus "pleasure, desire, lust"), from PIE *las- "to be eager, wanton, or unruly" (cf. L. lascivus "wanton, playful, lustful;" see lascivious). In M.E., "any source of pleasure or delight," also "an appetite," also "a liking for a person," also "fertility" (of soil). Sense of "sinful sexual desire, degrading animal passion" (now the main meaning) developed in late O.E. from the word's use in Bible translations. In other Gmc. languages, the cognates of lust tend to still mean simply "pleasure." The verb is first attested c.1230, "to please, delight;" sense of "to have a strong sexual desire (for or after)" is first attested 1526 in biblical use. Lusty (c.1225) mostly has escaped the Christianization of the word; the original usage was "joyful, merry," later "full of healthy vigor" (c.1374). The sense of "full of desire" is attested from c.1400.
That's a pretty dense block of text, so let me point out a really interesting bit: apparently the word "lust" originally just meant "pleasure" (or "to delight"), and still does in most Germanic languages. The connotation of "degrading", or even "sexual", comes because that's the word they used in the early translations of the Bible to English...
So now you know who corrupted lust. It was the Bible ;-)
That would also suggest that, as of the first Biblical translations to English, the phrase "the sin of lust" would mean simply "the sin of pleasure". Which means that phrase was already so clear that they didn't have to elaborate for everybody to figure out, "ah, okay, they mean sex" :-)
I'd go check the uses of "lust", but apparently this was noticeably before the King James -- that wasn't published until 1611, and uses "lust" pretty unquestionably as meaning sex or rape, at least according to me ogling a quick online search.