  We study the Lyndon interpolation property (LIP) and the uniform Lyndon
interpolation property (ULIP) for extensions of $\mathbf{S4}$ and intermediate
propositional logics. We prove that among the 18 consistent normal modal logics
of finite height extending $\mathbf{S4}$ known to have CIP, 11 logics have LIP
and 7 logics do not. We also prove that for intermediate propositional logics,
the Craig interpolation property, LIP, and ULIP are equivalent.
