Something to try:
1. Verify that you can get to the following URL in your web browser: https://www.arcgis.com/sharing/generateToken
This is the URL that Lumira connects to in order to initiate the logon workflow. If you cannot reach it in your web browser, Lumira likely won't be able to reach it.
2. Now check your web browser's proxy settings, and then make sure you have the same proxy settings in Lumira (under File > Preferences > Network).
If at this point you had to enable or change the Lumira proxy settings, click Done in the Preferences dialog box and restart Lumira.
3. Also double-check the credentials you typed in Lumira under File > Preferences > Geo Map Service. The Esri ArcGIS Online service treats not only the Password but also the User Name as case-sensitive.