I second Kazu. You will have to practice restraint to stay within $15 but their lunch menu makes it much easier.
McKibbons on Bishop also has a bar where you can eat. It won't be a diet lunch, but some of their food is not bad.
There is also Crescent street and you can sit at the bar at Wienstein and Gavino's - they have a 10$ lunch special.
1862 Sainte-Catherine St W, Montreal, QC H3H 1M1, CA