Discoloration after Cryotherapy. Will this ever fully fade?

If you had cryotherapy to remove lesions on your face it will behave like a scar. Wound healing can take 1-2 years to fully mature and reach the color which it will stay for some time. You are near the worst time for wound color, my experience has been that usually between 1-3 months people have the most "redness" of their wounds and it gets better from there.
Give it time.

Fractional laser is an amazing and highly effective treatment in our office. We use the laser treatment to help with acne scars, large pores, fine wrinkles, tissue collagen loss, scars, sebaceous hyperplasia, active acne, and for brightening dark pigmentation. Although there are very strong fractional lasers such as CO2 laser, we use lighter treatments for corrective skincare and maintenance of results. Our Thulium fractional laser, clear and brilliant laser, and Ultra Thulium laser are excellent options in our clinic. We also perform CO2 fractional and erbium depending on skin tone and tolerance for downtime. Patients do have to use a Melarase cream before and after treatment to help further reduce pigmentation after laser. Dark spots can improve with these treatments. I recommend fractional laser for incisional scars as well, especially after plastic surgery.

Best,
Dr. Karamanoukian
Realself100 Surgeon

That's hard and can happen. Sometimes you get red, then brown, then tan and pink. The good news is it should continue to improve though a year or more can happen...