I am Lerping the Near value of my camera, from 0 to 38, and it gives this result: change near clip plane effect
As you see, it gives a nice effect. But now I would like the effect to occur only for one specific layer. How can I do that?
Playing with Near/Far clip values by layers would basically mean to render every object using a different camera. Which would probably be overkill. I think what you're looking for is a custom shader on specific objects or group of objects that would "cut" them in given depth.
Please look at this very cool tutorial on how to achieve such an effect.