I doubt its laser based the issues with weather make Laser Guided weapons some what more problematic at sea.
I have not read of any orbital laser guided system. Data Link with GPS / Inertial is probably more likely. Terminal guidance by millimeter wave or other radar and or thermal/optical is fairly common.
LG weapons were the most accurate in Gulf War but the limitations made finding better solutions a priority.
Yup, perhaps there are multiple methods in use...in fair wx perhaps laser...in bad wx radar...etc.
Most satellites have orbital periods of in the single digit hours range. It would be able to laser designate the ship for ~10 minutes. And not whatever 10 minutes you want, but a specific time slot determined by the ships position and the satellite orbit.
The Tomahawk would have to be launched up to an hour before the satellite was over the ship. Not a very practical solution.
Of course if one had a large enough constellation of laser designator satellites, they could hand off the job to another one. I suspect the number would be more than 50, but less than 100. Again, not a very practical idea.