When you open LockDown Browser on your Mac, any custom settings you've made to the Touch Bar (such as adding Siri) will be removed temporarily. When the LockDown Browser session ends, those custom settings will be restored. However, to make those settings "live" again on your Mac, you'll need to do one of the following:
1) Restart the Mac computer.
2) Navigate to System Preferences -> Keyboard -> Keyboard tab
Select the pull down entry for ”Touch Bar shows” and check “Show Control Strip."