Like the Left Twist, the Left Purl Twist stitch creates a mock cable, crossing one stitch over the stitch to its left. With the LPT, however, the stitch in back is purled.
Working with the next two stitches on your left-hand needle, slip one stitch knitwise, then slip a second stitch knitwise, like the beginning of a ssk. Insert the left-hand needle into the two slipped stitches from right to left (so that both needle tips are pointing in the same direction) and slip them back onto the left-hand needle, reversing their order in the process. Now you can purl the new first stitch, then knit the second. Twist complete!
I haven’t found a good video showing this approach to the LPT. If you know of one, please let me know!