Is there a way to show the weather on the lock screen even when GPS is off?

Unfortunately, no. The lock screen's Weather Clock displays the weather of your current location so it needs Location in Settings to be always on.. You can, however, manually select your city in the Weather Clock widget on the Home screen so that it can show your local weather even if Location is turned off.

Important: To show up-to-date weather information, your phone must be connected to the Internet.

Here's how to manually select the city in the Weather Clock widget on the Home screen:

1. On the Home screen, drag the Weather Clock widget to Edit on top of the screen.
2. Tap the city whose weather you want to display on the widget. If you do not see the city, tap to add it.
3. Tap OK.

Note: If you want to turn GPS off, go to Settings, tap Location, and then tap the Location On/Off switch to turn it off.