We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical $r$-matrices with Poincae generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
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