I’d say the best way for a government to do this would be to mine with the excess energy of their grids. With each block found, or at the end of the week, divide and send out the rewards to each person.

Might not be possible over LN itself. Maybe it gets distributed to local government mints who then add credit to their jurisdiction recipients. Then the recipients can use it as they please.

Dividing between millions of people may create very small amounts like 1 or 10 sats, so the value of bitcoin would have to be significantly high than it is now, OR the grid mining farms are winning quite a number of blocks.