The phrase "in lieu" means "instead of" or "in place of". Time in lieu is given to someone who has worked extra hours (overtime). Instead of being paid for the extra hours, they are given time off from their usual scheduled hours. One usually has to work the extra hours in advance of getting the time off work. It can also be used in other contexts.... The Foreign Minister attended the conference in lieu of the President. In lieu of flowers, please make a donation to the hospital. I gave a laptop to my landlord in lieu of rent. When I won the competition, I was given cash in lieu of the prize holiday to Thailand.

"time in lieu" means time off work which you will have to repay at a later date. "lieu" means place, or instead. So you are somewhere else instead of at work.

Basically, you can't have the time off for nothing.