"during my lunch" is a correct and usable part of a sentence in written English.
For example: I enjoy catching up with my friends during my lunch break.
I made more money during my lunch hour than you'll earn in a decade.
"In recent years, I have been stopped during my lunch break at work.
But I can only do it during my lunch as I work in a busy retail store.
This photo was taken in March 2007 during my lunch break when I used to work in Sugar Land, Texas.
Ken and Paul came down on set and we went to a little cafe during my lunch break.
I went out and shot for half an hour, then came back and edited it during my lunch break".
To the food blogger whose Tumblr I've been following for three years: I want to read your mock-serious food-truck reviews during every one of my lunch breaks for the rest of my life.
In 1993 I struggled to find a restaurant for lunch during my break from classes.
When I was outed one afternoon at lunch during my senior year, my heart stopped.
I even skipped lunch during my senior year so that I could hear the AP Calculus lesson twice each day.
I broke out lunch during my visit to Bear Gulch Cave, sitting on a rock and chilling out in a fresh breeze.
