Hi Justin,
I understand that you encounter this error when performing migration. This error may occur when migrating a huge mailbox to Office 365, or the server is overloaded.
As this issue only occurs to one user, the direct and suggested way to achieve your goal is to export the live mail account emails to an .pst file and then import the .pst file to your Office 365 account.
After all of the mailboxes are migrated to Office365 cloud successfully, please stop the migration batch.
Thanks,
Amanda