A basket shows Lost when it has had both automatic reminder emails and the shopper still has not bought.
Lost does not mean gone. The basket stays in the list and nothing is deleted. You can still press Remind and write to the shopper yourself, and if they come back through a reminder's link and buy, the basket shows Recovered and the recovered cards at the top of the page go up.
If you set Reminders to First reminder only or Paused, baskets never get two reminders, so the Lost filter stays empty. That is expected.