Here is a scale diagram for the F Lydian scale on the C6 neck. The position begins with the root on the 10th string, and moves in a vertical direction.
This can help in visualizing this particular pocket of the fretboard, and can also help in memorizing the notes of the scale and the fretboard.
You can click on the image (on the attachment page too) to get a better view of the diagram. Enjoy!