The easiest way is to lift the whole plastic part where your gearshift is sticking through. You can simply pull it up, it's only hold down by some clips.
The reason for that is visible on the first pic.
Although the lighter isn't lit there is a thing on the side that allows a light to be fitted, quite useless, it's black opaque plastic.
But this thing is what's keeping you from just pulling the lighter socket out.
You will have to unplug the socket, remove the metal inner part first and then you can get the plastic part out.
Sounds easy but the metal part is hold back by two little plastic tabs you can barely see in the openings of the metal part.
If you push from the bottom and with a small screwdriver push against the tab you should be able to get the metal part out without damage. Then it's easy, just push the plastic part out, it is only hold down by two tabs at the outside of the plastic part.
There is a faster way and that is to just cut the useless side piece off and that way you can push the complete lighter out