Use 'lieu' to mean 'instead of' when you're talking about replacements or alternatives. They offered me extra vacation time in lieu of a raise.
Pro Tip 2/3
Formal situations
'In lieu of' is fairly formal; it's used in business, legal contexts, or serious writing more than casual conversation. In lieu of traditional proceedings, the company held a mediation session.
Pro Tip 3/3
Fixed expression
'In lieu of' is a set phrase; don't change its form. Don't say 'in the lieu of' or 'in lies of'. Guests are asked to make donations in lieu of gifts.