LocalDb is a packaging mechanism for SQL Server Express Edition, and is only available for Windows. On Ubuntu you can install regular SQL Server Express Edition.
https://learn.microsoft.com/en-us/sql/linux/sql-server-linux-overview
Here are the install scripts for Ubuntu, Red Hat, and SUSE.
Or use the Docker Images:
https://learn.microsoft.com/en-us/sql/linux/quickstart-install-connect-docker