Yes Leon your meaning could be right. It's hard to tell unless you supply more details. The sentence can also mean to sacrifice your time. A person on a diet might also throw away their lunch. As a teacher, I see many students throw away their lunches that have been made carefully by their parents and go straight to the canteen to buy junk food.

To "throw away" means to put something in the trash/rubbish/garbage. "I will throw away my lunch" means that you will put your lunch food in the trash, probably because you don't want to eat it anymore, maybe because you are not hungry or there is something wrong with it. If you actually can't go to lunchtime, then you simply "miss lunch."

Apparently somebody afraid to vomit after eating that kind of lunch.