How to not show different light sources in different cameras

I'm trying to implement a system where there are two cameras: main camera and secondary camera. Main camera shows the whole scene to the player while a secondary camera renders a portrait of a character (gameobject) in the UI by a render texture.

My problem: How to not show the main light in the secondary camera and the secondary light in the main camera.

I have tried different layers and culling masks but so far I haven't figured out how to not separate the light sources in different camera feeds properly.

Any help would be appreciated.

Here is a picture attempting to visualize the problem:

https://www.dropbox.com/s/f4rjajcblr28t8n/Unity%20problem.png?dl=0