A request for a LOW_PRIORITY WRITE lock, by contrast, permits subsequent READ lock requests by other sessions to be satisfied first if they occur while the LOW_PRIORITY WRITE request is waiting [to be granted].
Nothing is mentioned about an effect on WRITE
lock requests, so the LOW_PRIORITY
modifier has no effect on concurrent them.
The LOW_PRIORITY modifier has no effect as of MySQL 5.5.3
And:
As of MySQL 5.6.5, it is deprecated and its use produces a warning. Use WRITE without LOW_PRIORITY instead.