Just looking at 2 different guitar methods, I am a bit intrigued because it looks like the Lydian and Mixolydian shapes can have their notes played exactly in the same order in position 4 and position 5 so those 2 shapes can actually be "combined" to become one, depending on whether you play those shapes in the "3 notes per string" fashion or not ...

Here is what I mean, let's take the key of C major for example:

- 3 notes per string shape for F Lydian fingering (position 4):

---------3--------5--------7---------
---------3--------5----6---------
----2--------4---5---------
----2---3--------5--------
----2---3--------5---------
1-------3--------5-----------

- 3 notes per string shape for G Mixolydian fingering (position 5):

---------5---------7---8---
---------5----6--------8---
----4----5--------7-------
3--------5--------7-------
3--------5--------7-------
3--------5--------7-------

Now here is another fingering from another guitar method that combines position 4 and position 5 (thus giving us only one shape for both, instead of 2):

------3---------5--------
------3---------5----6---
2---------4-----5-------
2----3----------5-------
2----3----------5-------
-----3----------5-------

How is that possible?

that last one is not lydian because you are not using the F as a starting point. But you are in the right track, once you picture these clearly in your head you'll start become more fluent in them definitely.

F Lydian and G Mixolydian have the same notes as C Major, which means that the scale boxes will be exactly the same. This is the same for all the 7 modes of the major scale. The difference is which note you start on.