I realized my comments were better suited as their own answer.
You are absolutely correct that a hooded lantern would be visible in the dark from any distance. Assuming you had direct line of sight on the lantern.
So if you are in an open empty field, or a very large open cavern, then you are right...there's no point to a hooded lantern.
However, you can only see light if you have line of sight on it. And, when seeing 'light' there are two things you may be seeing. You may either be seeing the source of the light (the lantern) or you may be seeing the area illuminated by the light.
So, where this becomes useful is in areas that do not have clear, long-distance visibility. Such as in a building, or a cave, or a forest, or city streets, or literally anywhere that is not an open field.
The way this works is this: If you have a hooded lantern and you have the hood up, you are casting a Sphere 60' aura of light around you. In an area with corners, doors, or any other obstruction that blocks line of sight, this means any creature that can see any part of that 60' radius aura of light...can see your light.
However, if you hood the lantern, that drops it to throwing off a radius 5' aura of light. Bearing in mind that spheres include their origin as part of the radius...this means that only the single square that the lantern is sitting in is illuminated, with a bit of bleed-over into the neighboring squares. This means that unless a creature gets line of sight on the squares immediately around the one the lantern is in, they cannot see the light.
There are several practical uses for this. While dungeoneering, the party can dim the lanterns to sneak up to a corner. If each party member carries a lantern, they can each see where the other is, and see the ground under their feet so they don't trip or anything...but no one around that corner can see them coming, because none of the light created by the lantern reaches around the corner to become visible. Then the elf sticks their head around the corner, using their Darkvision to see what's there...all without ever showing any light to the creatures around that corner.
On the other hand, if you wanted to try the same trick with a non-hooded lantern, the party members that can't see in the dark would have to stay 60' away from the corner, so that the light created by their lanterns didn't go past it and reveal their presence.
So, in summary...
Yes, a light is visible from a tremendous distance, IF you have line of sight on the light source, or anything the light source is illuminating. In an open field, this means dimming your light doesn't help much. But in an area with obstructions, dimming your lantern means you reduce the aura that is visible in the dark from a 60' sphere, to a 5' sphere. And given that this aura can shine past corners, under doors, through windows, and so on....reducing your light aura is very useful in areas with obstructed vision.
Action Economy will prevent this combination.
Witch bolt states:
...you can use your action deal 1d12 lightning damage to the target automatically. The spell ends if you use your action to do anything else.
Emphasis is mine, to point out the problem- if you go invisible first, casting the spell ends your invisibility. If you go invisible after the initial casting of witch bolt, using your action to do so, you end the spell.
Yes, you remain invisible.
The text states:
We can break it up to determine how it works.
This is the only condition that must be met for you to become invisible. If you are in dim light or darkness, and you can take an action, you can become invisible full stop.
These are the only conditions that cause you to lose invisibility. The invisibility ends when you either move, take an action, or take a reaction. Transitioning from dim light/darkness to full light is not moving, taking an action, or a reaction, so the invisibility remains.
If you're worried about this being overpowered, remember that in 5E invisibility is not that useful by itself. It doesn't actually make you any stealthier or harder to detect than normal. The only thing it does is give people disadvantage against you (which is powerful no doubt), and it allows you to hide in plain sight. However, hiding is an action, which according to the text you quoted removes the invisibility. Since your Warlock can't hide without losing his invisibility, he will still be detectable by everyone around him. All this lets your Warlock do is get disadvantage on attacks against him as long as he doesn't move or take actions/reactions.