SQL Server job failure email without Internet connection We are using a local area network and we send emails through Outlook via Exchange Server. 

My question is can I get SQL Server job failure notification emails in Outlook via LAN (without an Internet connection)? And if yes, how?
You just need to enable mail profile and get the email exchange server IP and listening port as well as a valid active directory mail account for setting up email alert notification for jobs as well as alert on multiple things(dis.

Please check below link for setting up mail profile and operator:

https://www.mssqltips.com/sqlservertip/1523/how-to-setup-sql-server-alerts-and-email-operator-notifications/

https://sqlbackupandftp.com/blog/how-to-set-up-sql-server-email-job-notifications

For setting up notification on alerts:

https://www.sqlshack.com/create-configure-sql-server-agent-alerts/

Hope above helps.