A lack of correlation does imply a lack of causation
Correlation does not imply causation, but a lack of correlation does imply a lack of causation.
The famous maxim that “correlation does not imply causation” seems to get over-interpreted into some kind of suggestion that correlation and causation can never be related in any way.
One aspect of that is that a lack of correlation does imply that there is no causation effect going on. If there was a causative relationship between two things, we would expect to see correlation.
Seeing a lack of correlation between two things does imply that neither causes the other.