Summary: In studying the conditions for a poset to be a spectral space, W. J. Lewis and J. Ohm asked in Can. J. Math. 28, 820–835 (1976; Zbl 0313.13003): if the ordered disjoint union of posets \(X_\lambda\) is spectral, are the \(X_\lambda\) also spectral? There is so far no answer to this question in the literature. In this paper, we prove that in certain cases, the answer to this question is affirmative.