Do items you get from lunch boxes you buy appear in all vaults or do you have to buy them again. I'm just worried that when I buy some lunchboxes and my vault goes to the crapper I'll lose everything if I start a new vault.

no, they are stuck with the vault you opened them in

Like the other guy said, you are essentially screwed.

I do wish the legendary stuff can go across all the vaults.

Not only do you lose the items from the lunchboxes, it looks like you lose all unopened lunchboxes as well. I bought some and then created a second vault. The second vault is showing zero boxes.