Engine Coolant gauge reads zero and cooling fan stays on after shutoff.

[Ron Smith]

I just purchased a used 2017 Lacrosse preferred last week with 75k miles. This morning when parking at work, the radiator fan would not turn off for a solid 10 minutes. I did not use or need A/C during my 45 minute morning commute.

However during my lunch break, the A/C would not pump any cold air, and the right-most temp gauge never moved from the bottom.

The A/C has been working great all week up until now. I've only ever bought used cars, but this is a new record for me in terms of how quickly a problem appeared after purchasing a vehicle. I'll be sure to check radiator fluid after reading some of the above anecdotes.

This is a very common problem with the 2017 & up Lacrosse and cost around $1200 to fix since the intake manifold has to come off and is labor intensive. It probably won't happen every time you drive the car. If you disconnect to battery, for longer than 15 minutes, you'll reset everything and you should be good for a few drives but it will come back.
You said that you just bought it? Did you buy it from a dealer? There might be a 30 day warranty? But if not, I would see if they would cover some of the cost. Good Luck!