The dominant Lydian mode corresponds to the fourth mode of the melodic minor scale. This mode, frequently used in Jazz, has the peculiarity of being close to the Mixolydian mode. However, the only difference is that it includes a higher fourth (hence the term "Lydian") while the Mixolydian mode comprises a perfect fourth. This mode can be used on a dominant seventh chord, and will have the feature of bringing out the higher fourth, thus the Lydian feel and sound. It is also the mode that best corresponds to a seventh chord with a higher fourth or diminished fifth.
You'll find below the 5 different positions/shapes of the A Dorian #4 Uke scale in Slack-key Tuning (gCEG), along with their ascending tab patterns.
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