I haven't been able to make it to a cheap lunch yet. Best I can do is a turkey sandwich with lettuce, tomatoes, and lemon. And some chips. Works out to about $5 a lunch. I'd rather work on the income side of things and if I need to spend money to not eat PB&J or Ramen, fine. I just haven't gotten to the point where I'm willing to forgo meat to save money, can't bring myself to do it.
$5 would mean you can have a pound of chicken and a pound of cheese on your sandwich... At least in my area.
I typically eat one of two things for lunch.
1) left over home made pizza at less than $0.62/slice (so $1.24 for lunch)
2) Chicken wrap with lettuce, onion, and tomato. Probably ~$2, made out of home cooked chicken breast ($2/lb), peperjack cheese ($3.50/lb), burrito wrap, lettuce, onion, mayo, and sometimes tomato if we have it.
Always eaten with 32oz home made iced tea at less than $0.25.
So for you, you'd probably save a bit of money if you switch off of expensive lunch meats. Roast Beef is my go to lunch meet, but is closer to $9/lb where as uncooked boneless chicken breast is $2/lb and I love chicken so it works for me.