[RPG] Contesting Casts of Control Weather

First of all, there is nothing in the spell description that suggests that "control over the existing storm instead of creating a new one" does anything other than subvert rather than create the same "storm cloud" described in the first paragraph. If there is already a cloud 100 feet above your head you get that one (and the extra damage); if not, you create one. So the answer to your question is the same in both cases.

The spell's description says:

When you cast the spell, choose a point you can see within range [120 feet]. A bolt of lightning flashes down from the cloud to that point. ... On each of your turns until the spell ends, you can use your action to call down lightning in this way again, targeting the same point or a different one.

There are two things to consider:

Range

The target of a spell must be within the spell’s range.

Once a spell is cast, its effects aren’t limited by its range, unless the spell’s description says otherwise.

"in this way again" means that range is still a factor. And this tweet (apart from the fact that the range is misquoted) indicates that the range is measured from you - not your storm cloud:

@mikemearls As a follow-up, as long as you can see a target within that 60 ft. radius, you can move as far away from the storm as you want?

@TheShieldComics Yes

Target

To target something, you must have a clear path to it, so it can’t be behind total cover.

I think that in the case of this spell it is the cloud, rather than you, that must have the clear path.

Is there a restriction on the location of where the spell caster can call lightning down from when the lightning is called down from a natural storm in stormy weather?

Yes, the target must be within 120 feet of you and have a clear path to the cloud

So yes you can do exactly what you want - move up to 3000 feet and keep calling lighting from your pet cloud that is 3000 feet away. Given that a lighting leader travels at 61 km/s and the return stroke at 27,800 km/s; the lighting will take about 15 milliseconds to make the journey - well within the 6 second round. You can do this irrespective of if there was a pre-existing storm or not.

It's very reliable. According to the description, it "predicts what the weather will be". No ifs, ands, or buts. This suggests perfect accuracy.

That said, it's not very precise. (Precision is not the same as accuracy.)

The description isn't clear whether it shows a single effect that predicts the weather over 24 hours, or if it changes in appearance over the course of the round (6 seconds) depending on the weather. Either way, if it shows you that you have a cloudy night, that doesn't mean it will be cloudy for the entire night, or at any particular moment. So if you're sneaking into a castle, be prepared for the moon to shine through an inconvenient gap in the clouds.

Similarly, it says it shows the weather "at your location". This is equally imprecise - it could be anything from the exact point you're standing at the time to the entire region you happen to be in. In the first case, unless you snuck into the castle to do your weather prediction for sneaking into the castle, be prepared for the weather to be a little bit different. In the second case, you only have a very vague idea. The city where I live often predicts rain, but I don't often see any - it mostly rains down the south end.