Using classic Outlook for Windows in business environments
There is no way to just delete live.com e-mail account but keep hotmail.com account. They are basically the same account since Microsoft has merged Hotmail.com, live.com, msn.com into outlook.com. Existing Hotmail, Live, Outlook.com, and MSN addresses can't be added as aliases, and you can't add an alias that is already associated with another Microsoft account. Also, it isn't possible to create a new aliasusing @hotmail, @live.com, or @msn.com. If a Hotmail address is important to you, you need to sign out and create a new account.
If you would not like to give up Thunderbird or your Microsoft e-mail account, then I'm afraid you will need to wait for Microsoft tech team to fix this unusual activity issue.