Borger’s theory of Lambda-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by F1-geometry and monoid schemes, we prove the existence of resolution of singularities in the category of Lambda-schemes. In this talk, following arguments based on Hironaka’s proof of resolution in characteristic 0 we first produce a weak Lambda-resolution from the order reduction of an ideal marked with Lambda-equivariant data. Restricting to toric Lambda-schemes we then prove a stronger resolution theorem based on work of Bierstone and Milman for toric varieties.