I may be dating myself but if your remember the 1970's group The Little River Band" they had a song called "Love Takes Time." In Dermatology, legs take time. The lower down the leg, the longer it takes to heal. Usually scabs are healed within about 3 weeks. Discoloration can take several months to subside.
It usually takes 3-4 weeks for the brown spots to peel or scab off after liquid nitrogen treatment. Depending on your skin type, you may have some redness or pink discoloration for months after the treatment. This can be normal. If they don't clear up in the next few months I would recommend that you go back to your dermatologist for follow up.
After liquid nitrogen treatment, a sore or scab may persist as long as 3 months on the lower leg because healing in this site is often slow.