Some men are terrible at knowing that a woman is flirting with them (i am in this category) so he may be unaware of the situations like that that bother you. 

It is however a very reasonable request IMO that he not meet repeatedly with *only* her for lunch.  Once in a blue moon, sure.   Weekly, no.   I am sure some will say thats ridiculous, but i personally would rather not give my SO anything to worry about as i would appreciate the same in return.   


Just tell him that are uncomfortable with him having lunch with only her on a regular basis.    He may be entirely oblivious to the fact especially if you are more attractive and younger than her (in his mind she would be a total non-threat).