The Read-only lock should be removed from your source site collection or columns before running a migration action with the ShareGate migration tool.
The ShareGate migration tool accesses SharePoint through multiple APIs and has to send many requests to the servers to obtain and resolve your data. Given the complexity of this operation, a read-only lock will often cause one of these calls to be unresolved, and the ShareGate migration tool will be unable to push the data properly. This results in errors, and some items may not copy properly.
Some SharePoint services do not respond correctly when the site collection is on read-only mode (even if they are only used to read information), and the requests will not be processed as intended.
To prevent users from editing data stored in a field, you can set site columns as read-only through PowerShell or CSOM. By modifying the column to be read-only, ShareGate cannot access the information.
You must remove the Read-only lock on your site collection before running your migration. You can do so by following the instructions outlined in this article. Not removing the read-only lock will mostly affect the structural parts of your environment, like Web Parts and Site settings, but the behavior is unpredictable and it may affect more overall.
For read-only columns, if the column can be changed to the default state you should be able to migrate your data successfully.