You can use the weather widget on the lock screen, and as long as you have lock screen content when locked enabled, you can see the current area's weather just fine. Or do you want the whole app experience?

The lock screen widgets don't tell you much more than what you can get from looking outside. It's not very helpful to know that it's currently overcast and raining, but it would be a lot more helpful if I could know when the rain is supposed to stop or what the week's forecast is and so on.

I'm a little too lazy to experiment, but it wouldn't surprise me if that widget didn't function normally until the phone is unlocked.