A projective cover in a category, J%Γ, of algebras is a morphism φ\P-> A where A, Pe-%^, P is projective in JfΓ and no proper subalgebra of P has A as its direct image under φ. Projective covers of finite distributive lattices in the categories *£?, of all lattices and -S^πn of all finite lattices are determined (when they exist).