When connecting Outlook/Office 365 account with a standalone LiveAgent license installed on your own server, please see this article.
LiveAgent uses Microsoft OAuth authentication to connect with your Outlook/Office 365 accounts. After you authenticate this connection in a pop-up window, your Outlook/Office 365 mailbox is connected, and no further configuration is needed. Just follow these simple steps:
In your LiveAgent account, navigate to Configuration > Email > Outgoing Mail accounts, and click on the "Integrate new email account" button.
In the left "Mailbox account" section, use the Microsoft connector to connect your Outlook/Office 365 account.
On the next screen, click on the "Connect" button. It will automatically open a pop-up window with a Microsoft login page, where you need to log in to the Microsoft account that you want to connect as an outgoing email account and grant LiveAgent access to this account. After successful authentication and login, the pop-up window will be automatically closed.
If you'll get a message "Need admin approval", you are not allowed to integrate this email account and would need to contact the administrator of your company's mail accounts to resolve it.
After the pop-up window is automatically closed, Finish the integration in LiveAgent.
That's it, your Outlook/Office 365 account will be successfully connected with your LiveAgent account, and you can start sending replies to your tickets/emails through this mail account directly from LiveAgent.