Yes, if you have set up and enabled Touch ID for your macOS, you can use Touch ID to unlock your LastPass Mac App and access your Vault as long as you are on one of the paid LastPass plans.
Please note: Touch ID for Mac can only be used for unlocking the LastPass Mac App.
For more information and steps for how to set up Touch ID for the Mac App, please see here: https://support.logmeininc.com/lastpass/help/how-do-i-set-up-and-use-touch-id-for-the-lastpass-mac-a...
Thanks for that additional info.
Just to be sure, could you make sure that Touch ID for macOS is set up first and then restart your computer, then re-launch the LastPass app to see if the option shows there after the restart? Could you also try uninstalling the LastPass Mac app by dragging the LastPass app icon in Finder > Applications to the trash, restarting your computer, and then reinstalling the mac app from here https://lastpass.com/misc_download2.php to see if you then have the Touch ID option in LastPass preferences?