A classical topic in spectral theory is Weyl’s law describing the asymptotics of the eigenvalues of the Laplacian on a bounded open set. We are interested in these asymptotics in low regularity situations. Both in the Dirichlet and in the Neumann case we show two-term asymptotics for Riesz means of any positive order under the assumption that the boundary is Lipschitz continuous. For convex sets we obtain universal, nonasymptotic bounds. Tools in our proof are universal heat kernel bounds, as well as Tauberian Remainder Theorems.