  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 Poinca\'e
generators. As other examples, we present Lax pairs for pp-wave backgrounds,
the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
