You can install binary and platform updates to all (MS and cloud hosted) environments from LCS.
In any environment's details page, you can see the update tiles - they will direct you to a page where you can select the updates that you want to take. Note that these updates are cumulative so you will get all hotfixes and features that were released before the hf that you select.
After selection, a package will be created to your asset library. Apply this package to the environments that you want to update.
Note that the build server should be updated after test/prod or your newly built packages can't be deployed to test/prod anymore because of version mismatch.