The classical Chow form encodes any projective variety by one equation. We here introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates, we obtain universal projection formulas. These were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra, and we develop his approach further. Universal formulas for branch loci are obtained from Hurwitz-Lam forms. Our focus is on computations and applications in geometry.