Lyndon interpolation property for extensions of S4 and intermediate propositional logics

We study the Lyndon interpolation property (LIP) and the uniform Lyndon interpolation property (ULIP) for extensions of S4 and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite height extending 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.