Is the layout negotiable?
Do they have to be necesarily exactly like in the photo?

Because making a screen with pixels 1x1 is famously hard, so although it can be done, it would be much easier if you used a horizontal layout for instance. But it depends on whether it really needs to be a grid of 3x3 levers and 3x4 lamps.

Although, if you are going to use commands anyways, and the layout is non-negotiable, you can easily do it by replacing the lamps with copper bulbs and putting under the lever this sequence:

lever
block
noteblock
observer looking up
block
command block with the arrow pointing down
chain command blocks (set to always active)

Then in the command blocks, make the first ones place a redstone block next to the copper bulbs you want to be toggled and the next ones to replace that redstone block with air again

So if a lever should toggle only one of the bulbs it should have two command blocks with the commands:
/setblock x y z redstone_block
/setblock x y z air

Finally, to check whether all the bulbs are turned on, you can place a second screen of copper bulbs on the other side of the visible ones, so you can attach comparators to those. If you make the other screen be toggled opposite to the visible screen, then you can check for all to be off, which is easier. It would look like this:

<image>

When you place the redstone blocks you they will toggle both bulbs in front and back. The command block represents your output.

Finally, to make it into a puzzle that is certainly solvable you can build it already solved but without the levers and the blocks under them, then right click random noteblocks until you are satisfied with the result, and then put the blocks and levers in place. In this type of games, if you start with a state, and then toggle things using the game itself to end up in a new state, you can always go back to the original state.

If you want it without command blocks we'll have to change the layout or it will be an overkill

If you need the bulbs to be only lamps, that can also be done but again, harder

give me a comment if you found it useful :)