That's not how "lock free" is defined/used. If you are considering the MESI M state to be a "lock" then you also have to grant that any write instruction is a "lock".

In fact this a crux of the problem in low latency code and there are ways to combat this.

I know there is an academic wait-free and lock-free definition but folks use those often incorrectly as a slogan that something is magically better because it’s „lockfree”.

Imagine how _you_ would implement a read-modify-write atomic in the CPU and why E stands for exclusive (sort of like exclusive in a mutex)