Lascoux polynomials simultaneously generalize two famous families of polynomials arising from geometry and representation theory: They are non-symmetric analogs of Grassmannian stable Grothendieck polynomials, which represent Schubert classes in the connective K-theory of Grassmannians. Additionally, they serve as non-homogeneous analogs of key polynomials, the characters of Demazure modules. Both of these families have classical combinatorial formulas involving tableaux. We further generalize several of these formulas by establishing two combinatorial formulas for Lascoux polynomials.