Lapwing loses it, twisting to give cry (4)
I believe the answer is:
weep
'cry' is the definition.
(synonyms)
'lapwing loses it twisting' is the wordplay.
'lapwing' becomes 'peewit' (synonyms).
'loses' suggests deleting specific letters.
'twisting' says the letters should be written in reverse (letters twist back).
'peewit' with 'it' removed is 'peew'.
'peew' written backwards gives 'WEEP'.
'to give' acts as a link.
(Other definitions for weep that I've seen before include "Greet" , "Pee-pee" , "Display sorrow" , "Express grief or sorrow" , "Keen" .)