Hi thebook4, and welcome to this board.
Yes, you can do this , here is how it works :
1- Open Live on a blank set, go to preferences / link-midi
2- in midi ports menu, set minilab mkII input and remote on "on".
3- close prefs, and go in options and choose edit midi map ( or press ctrl+m to access it directly)
4- The mappable buttons will appear as purple, click on the desired transport button, and then press the desired pad on the minilab
5- Once done , you'll see your midi mappings in the left panel.
6- once you've mapped all desired transport buttons to the corresponding pads, go back in preferences/file folder
7- on the first line " save current set as default" , click on save.
From there, if you close and reopen live, this configuration will be the default template. After some creation using this template, if you save your live set, these settings will be recorded.
You can also start your mapping from an existing project: open your project, repeat steps 2 to 5 , and save your live set.
Please note that the midi remote script for the minilab mkII should be implemented of the release of live 9.7.2
hope it helps,
best,