No doubt she needs an increase. Better yet would be to also add a source of T3.
Everyone can have different thyroid hormone levels at which they feel their best, but your friend's results are much too low for most people. The doctor should be titrating her thyroid med dosage based on symptoms not based on blood test results. The objective of treatment is relief of symptoms, not just getting her test results within their ranges. Due to erroneous assumptions used to establish ranges they are far too broad and skewed to the low end, so moat people do better when their Free T4 is at mid-range, and Free T3 in the upper part of its range, and adjusted from there as needed to relieve symptoms.. She can get some good info from this following link to a study in which they quantified for the first time the effect of Free t3 on the incidence of thyroid symptoms.
https://www.ncbi.nlm.nih.gov/pubmed/29396968
In the link note the following: "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range. "
In addition to getting her fT4 and FT3 to levels adequate to relieve symptoms, she needs to supplement her Vitamin D to achieve a level of at least 50 ng/mL. She also should test for B12 and ferritin and supplement as needed to optimize. B12 should be in the upper end of its range, and ferritin should be at least 100.
The main thing she needs is a good thyroid doctor that will treat clinically (for symptoms).