How do I get lunch boxes without paying, do I wait for more dwellers to show up?

The objectives. Higher difficulty ones give free lunch boxes.

Nibble: Check out the 3 'quests' you have. Sometimes they reward free lunchboxes. Also every 7 days you will get a lunchbox for free for keeping your vault going so long. I was very lucy as my first Lunchbox ever game me 3 Dog. Then he died and I never brought him back.

Lol