TW3L does this mean that I turn the cable needle to the left.
I have no idea, what does your pattern say? It should have instructions for this stitch in the abbreviations.
I would assume that it is a twist stitch and that it involves 3 stitches, but that is just a guess. Usually, the L or R indicates the direction of the twist. In a left twist the stitches on the cable needle are held at the front and when the stitch is completed they lean from the right to the left.
In a right twist they usually lean from left to right and the stitches on the cable needle are held at the back.
But unless I can the pattern, I am only guessing and cannot be sure what the person who created the pattern intended.