Keen lapwing drops it, heading west (4)
I believe the answer is:
weep
'keen' is the definition.
(keen can mean to cry or lament)
'lapwing drops it heading west' is the wordplay.
'lapwing' becomes 'peewit' (synonyms).
'drops' indicates named letters should be taken away.
'heading west' says the letters should be written in reverse.
'peewit' with 'it' taken away is 'peew'.
'peew' back-to-front is 'WEEP'.
(Other definitions for weep that I've seen before include "Bawl" , "Greet" , "Display sorrow" , "Seep slowly out" , "Keen" .)