Laser hair removal burn marks - Are these marks permanent or is there another lightening process to get my legs back to normal?

Hyperpigmentation and inflammation after laser procedures is quite common. In general, hyperpigmentation of any kind needs a combination approach of peels like Cosmelan, lasers like Clear + Brilliant, Aerolase and Laser Genesis, radiofrequency treatments like Venus Viva, and constant skin care and sun protection. Bimonthly facials with SilkPeel / DermalInfusion are essential to hydrate, exfoliate and infuse vitamins and antioxidants into the skin. I suggest getting a formal evaluation with an expert in lasers and peels. Best, Dr. Emer.

Thank you for your question and posting pictures.  I'm so sorry this happened to you.  It looks and sounds like you might have Post Inflammatory Hyperpigmentation (PIH).  PicoSure Flat or FOCUS lens treatments should be able to take care of it easily with almost no risk.
FOCUS lens treatments have the extra benefit of reducing the underlying scar tissue.  This is one of our go to treatments for patients older than 40 and worried about the signs of aging.  This laser is safe for all skin types.  Start with sunscreen every day!  Once you have treated your hyperpigmentation to your satisfaction, you will probably need a follow treatment every 6 to 12 months depending your level of re-pigmentation.  Best of luck.