Let $${\text {Lip}}^n(X, \alpha )$$ be the algebra of complex-valued functions on a perfect compact plane set X, whose derivatives up to order n exist and satisfy the Lipschitz condition of order $$0<\alpha \le 1$$ . We establish a necessary and sufficient condition for a weighted composition operator on $${\text {Lip}}^n(X, \alpha )$$ to be compact. To obtain the necessary condition in the case $$0<\alpha < 1$$ , we provide a relation between these algebras and Zygmund-type spaces $$\mathcal {Z}_n^\alpha $$ . We then conclude some interesting results about weighted composition operators on $$\mathcal {Z}_n^\alpha $$ and determine the spectra of these operators when they are compact or Riesz.