You can re-trace your steps and cover a basic Lydian Mode here if you want to start with something a little easier. The minor version of the Lydian scale is fairly difficult, though can be easily mastered with time and careful playing.
Check the chart before you play, and plan out how you want to attack the scale based on the fret span of the notes on a given string. For example on the sixth string (thickest one) there are notes on the 3rd, 4th and 6th frets. Hence you should plan to play those strings with your pointer, middle and pinky fingers.
Follow suit when you consider the rest of the strings and notes. Here is the scale chart in the key of C positioned on the 3rd fret.
Your difficult spots here will be on the fourth and first strings, so come up with a plan of attack while examining the chart and then implement it slowly. Once you get comfortable with the pattern you've adopted, you can start to pickup speed.
Lydian Augmented Mode
Ascending Melodic Minor
Descending Melodic Minor