  We study various properties of the gradients of solutions to harmonic
functions on Lipschitz surfaces. We improve an exponential bound of Naber and
Valtorta on the size of the superlevel sets for the frequency function to a
sharp quadratic bound in this setting using complex analytic tools. We also
develop a propagation of smallness for gradients of harmonic functions,
settling an open question in this setting. Finally, we extend the estimate on
superlevel sets of the frequency to more general divergence-form elliptic PDEs
with bounded drift terms at the cost of a subpolynomial factor.
