Pigeon house on lake left incomplete (5)
I believe the answer is:
homer
'pigeon' is the definition.
(homer is a kind of pigeon)
'house on lake left incomplete' is the wordplay.
'house' becomes 'ho' (abbreviation for house).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'lake' becomes 'mere' (mere is a kind of lake).
'left incomplete' means to remove the last letter.
'mere' with its last letter removed is 'mer'.
'ho'+'mer'='HOMER'
(Other definitions for homer that I've seen before include "pigeon, maybe" , "returning flier" , "Pigeon; classic writer" , "Greek author; pigeon" , "makes round trip by air" .)