Solution (after some heavy hinting from the OP):
Here's how you decode the cipher:
You want to get three Imgur links to three images of green lamps. Each $5$ number group corresponds to one URL. Start from the original red lamp image URL ($pqvZn$), convert it to numeral ($a=1\dots$), add the numbers of each cipher and convert it back to letters (mod $26$) preserving the original capitalization (for example for the first one you get $xdzHx$) and then change the capitalization of each letter that doesn't correspond to a double digit number ($07$ is considered a double digit number and that's what the hint $8\neq 08$ is supposed to mean).
My opinion on the puzzle:
This puzzle looked like it was well crafted, but the cipher is really bad. A good cipher should be capable of encoding any type of message and this one can't. For example you if one of the solutions had a $D$ as a second letter you wouldn't be able to encode it with this cipher because writing $13$ doesn't change the capitalization. All you can get $q\to d$.
Old (and wrong) line of reasoning:
Start from the Red to Green image. I think this means what to open the door we need to turn those red light into green ones. How do we do this? By decrypting the message on the bottom on the paper. You can see that it is made by $15$ numbers divided into $3$ group of $5$ numbers. Also you can note (thanks @GarethMcCaughan)the string "pqv" that is the first three letters of the Imgur link of the red lights. Putting this all together makes me think that the solutions will be made of three Imgur link of three images of green lights that you get by assigning a value to each number of the code.
Each Imgur link is made of 5 characters that can be letters $a,\,\dots,\,z,\,A,\,\dots,\,Z$ or numbers $0,\,\dots,9$. Here is where I think the clue $8\neq 08$ fits. I think that $8$ means "this is an encoded letter" and "$08$" means "this is the number $8$ on the URL". This means that so far we got the three images:
Now, how do you decode the letters then? Since my hypothesis is that you need to change the red lights into the green ones I think you should start from the original image URL and change those letters by subtracting the cypher number from its value (a=1, b=2, ...). This might be confirmed by the $d$ over the number $13$. The original URL is pqvZn. If you take the second letter $q$ and you subtract $13$ you get $d$. Since all the three red lamp images are the same you need to start from the same URL in all the three cases.
If you do this for all the numbers here's what you get:
But none of those images actually exists. As you can see I'm obviously missing the capitalization of the letters. I don't know whether a letter will be lowercase or uppercase. If I preserve the capitalization of the original URL (so only the 4th letter will be uppercase) I still get nothing.