Besides adding a stick-on LED strip lighting kit to the underside of the awning, you may want to consider adding LED lighting to the end of the awning arm.
You need to purchase Valterra A30-0600 Rope Light Trak from amazon...
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
This consists of a number of 3 foot segments of plastic that slide into the awning roller assembly that will give you two fittings. One fitting will allow you to string LED Rope lighting, while the other fitting gives you the ability to purchase a sun screen fabric and insert it to be held up by the awning. You can see my sunshade setup below. The rope lights wound around the awning arm is just visible.
You then have the ability to snap into place whatever type of LED Rope lighting you would want in any color... bright white or colored. These rope lights are powered with 120 VAC, not 12VDC, so I start with the rope light supported by the awning arm and plugged into an extension cord.
I typically string a subdued red rope light from the awning arms, across the inside part of the awning, and back toward the trailer on the opposite arm. However I also have a blue rope light string, which I occasionally use.
Snapping the rope light in or out of the rope light trak is quick and easy. I leave the track in place while rolling back and storing the electric awning, although you do have to remove the rope lights when retracting.
I ordered the track I am using back for the 2015 season, and just used them within the past month in 2018 again and they are holding up.
Rope lights can be ordered from Amazon and I have seen them also available at Home Depot typically in the white light variety.
I hope this helps give you another option for LED lighting.