He has a meal without me at lunchtime (3)
I believe the answer is:
ali
'he' is the definition.
'a meal without me at lunchtime' is the wordplay.
'without' is a deletion indicator.
'at' says to put letters next to each other.
'lunchtime' becomes 'i' (1pm could be I on a clock with Roman numerals**).
'meal' with 'me' taken out is 'al'.
'al'+'i'='ALI'
'has' is the link.
(Other definitions for ali that I've seen before include "Muslim name" , "Champion of ring" , "Ringmaster" , "Son-in-law to Muhammad" , "Muhammad --, US boxer" .)