"Lunch on your own" indicates there will be a planned stop where you can purchase food.

“早餐自理”就是说我们会计划在某个地方停留一段时间以方便大家购买食物。

youdao

You know, I try very hard to make our lunch hours educational and informative, but your insistence on talking about your own lives stymies me at every turn.

你们知道，我非常努力尝试着，使得我们的午餐时间能有教育性和有见识性，但你们每次都坚持用自己的私生活，来阻碍我。

youdao