Yes, the GPS needs to be on all the time, which by way of experimenting, I have discovered that just leaving it in High Accuracy Mode versus it being OFF only makes about 20-30 minutes difference in battery life overall.
So, I don't turn it off anymore.
IIRC, it is tied to AccuWeather and that is indeed the case, as the screenshot shows. Look at the bottom of the screen, it names the widget that is providing that info.
IIRC it is only programmed to update on 30 minute increments. There is a Refresh Symbol on the homepage that will cause it to update with the latest recorded info.
For myself, I turned off the Weather display on the Lockscreen for the reason you mention. It is out of step too much. Especially for me because I keep data turned off all the time.