A 'day in lieu' means that if you're forced to work a day you were supposed to have off, you can take a day off you were supposed to work in the future. For example, you normally only work Monday to Friday. You are asked to come in on Sunday, with a day in lieu. This means that in return for working Sunday, you can take day off during your regular working week.
Does that clarify it? What would you call this arrangement in the states?