Unhappy, oddly lacking sleep (3)
I believe the answer is:
nap
'sleep' is the definition.
(a nap is a short sleep)
'unhappy oddly lacking' is the wordplay.
'oddly lacking' means one should take alternating letters (letters in odd-numbered positions removed).
The alternating letters of 'unhappy' are 'NAP'.
(Other definitions for nap that I've seen before include "Short sleep, card-game" , "Kip" , "Racing tip that claims to be a certainty" , "Short sleep on soft surface texture?" , "Siesta" .)