If Him saying "I change not" is inherently change, then "I change not" is automatically ipso facto a lie.
False dichotomy.
The alternative is that God is saying that He does not change in a certain way, but that certain way does not include the change of speaking.
The CONTEXT of the verse shows us just that.
So does God lie, or does God not change. It can't be both.
Still a false dichotomy.
The alternative is that God DOES change, but not in the way that the context is talking about, and that He does NOT change in the way that the context IS talking about.
In other words, God changes in some ways, and not in others.
https://opentheism.org/verses lists 33 different categories of verses that support the notion that God is free, which includes the fact that God does change, categories 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, and 33 all contain verses that directly or indirectly show God as changing.
27 is a category that contains a verse that describes men as unchanging (Psalm 55:19).