You have to pass the main PApplet object or the main canvas to your library, like this
MyLib myLib = new MyLib(this) /new MyLib(g)

In your lib you can use yourPassedPApplet.g.pixels[] or g.pixels[]

I have encountered situations where a library offers several different classes, and in order to avoid having to pass the PApplet to each class, I had a static property and init() method containing the PApplet:

Code:

public class MyLibrary{
  static PApplet parent;
  
  public static class LibraryNotInitializedException extends NullPointerException{
   LibraryNotInitializedException(){
     super("Must call MyLibrary.init(this); before using this library.");
    }
  }

  static void init(PApplet _parent){
   parent = _parent;
  }

  static PApplet parent(){
   if(parent == null){
    throw new LibraryNotInitializedException();
   }
   
   return parent;
  }
}
 

From inside the library then you can access the pixels by doing:

Code:

for(int i=0; i<MyLibrary.parent().pixels.length; i++){
  MyLibrary.parent().pixels[i] = 0F;// paint the pixels of black
}
 

From Processing you would always have to initialize your library before using it:

Code:

MyLibrary.init(this);
 

This method has the advantage of only having to pass the PApplet once, instead of at every constructor.