Etymology
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lassitude (n.)

early 15c., from Latin lassitudinem (nominative lassitudo) "faintness, weariness," from lassus "faint, tired, weary," from PIE *led-to-, suffixed form of *led- "slow, weary" (source also of Old English læt "sluggish, slow;" see late (adj.)), from PIE root *‌‌lē- "to let go, slacken."

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*‌‌lē- 

Proto-Indo-European root meaning "to let go, slacken." 

It forms all or part of: alas; allegiance; lassitude; last (adj.) "following all others;" late; latter; lenient; lenitive; lenity; let (v.) "allow;" let (n.) "stoppage, obstruction;" liege.

It is the hypothetical source of/evidence for its existence is provided by: Greek ledein "to be weary;" Latin lenis "mild, gentle, calm," lassus "faint, weary;" Lithuanian lėnas "quiet, tranquil, tame, slow," leisti "to let, to let loose;" Old Church Slavonic lena "lazy," Old English læt "sluggish, slow," lætan "to leave behind."  

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languor (n.)
c. 1300, "disease, sickness; distress, mental suffering," from Old French langor "sickness; weakness" (12c., Modern French langueur), from Latin languorem (nominative languor) "faintness, feebleness, lassitude," from languere "be weak or faint" (see lax). Sense in English shifted to "faintness, weariness" (1650s) and "habitual want of energy" (1825).
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