Yes, accordingly to the documentation Lifecycle actions:
For buckets in a region, the new storage class cannot be
Multi-Regional Storage.
As result, if you want to use Lifecycle to manage Storage Class of your data you should switch to using the same location region or multi-region. More information you can find in the documentation Bucket locations:
Use a region to help optimize latency and network bandwidth for data
consumers, such as analytics pipelines, that are grouped in the same
region.
and
Use a multi-region when you want to serve content to data consumers
that are outside of the Google network and distributed across large
geographic areas, or when you want the higher availability that comes
with being geo-redundant.
As a possible workaround you can try Storage Transfer Service:
Storage Transfer Service allows you to quickly import online data into
Cloud Storage. You can also set up a repeating schedule for
transferring data, as well as transfer data within Cloud Storage, from
one bucket to another.
You can schedule daily transfers between your region and multi-region buckets using as filter like Filter transferred files by last-modified time with Min age and Max age in hours, and options like Delete objects from source once they are transferred.
