Further to my previous post, I checked the configuration on my Macbook Pro. I found that TouchID wasn't enabled in my system preferences (though it had previously been setup). Maybe this was disabled in some update of the OS. When I enabled this, I found that the checkbox was no longer greyed out in Lastpass, and I could select the flag. I did that and now can use my fingerprint to authenticate with lastPass on my Mac!
So, I apologise to Lastpass as I believe this was an issue on the Mac, not with their application.
Maybe it would be a good idea to put a message next to the greyed out box saying "TouchID is not currently configured for this Mac. Go to system preferences to setup". This would then advise what the issue is and point the user to the cause / resolution.
Hope this helps anyone having the same issue as me.