Not to diminish O-3/O-6 balance as an important health consideration but the thing that helped me the most (and frankly, the ONLY thing) was the implementation of a gluten-free, yeast-free diet. I'm now eating about 97% grain/legume/soy/sugar-free, but I found the most significant effect from the initial changes.
For many years I was on medication for depression, and subsequently anxiety and bi-polar II, with negligible-to-no positive outcome. Currently I take no pharmaceuticals, and am more mood-stable than I've ever been in my life. 95% asymptomatic. I now recognize depression, anxiety, and hypomania as a direct function of the food and drink I consume, and the quality of my sleep.
Proper nutrition should be the cornerstone of treatment for any health problem, yet MDs are not required to learn anything but the food-pyramid basics. Furthermore, there is an important link between gut-health and mental-health that is being all but ignored by the increasing specialization of western medicine. [Just ask the celiacs with neuro-problems how long it took to get a diagnosis - and then ask them about the prescription.] The pharmaceutical industry basically writes the DSM, and the diagnoses therein should be trusted accordingly.
Your mom should certainly start supplementing with O-3, especially if she eats the SAD, and her Dr. is one-in-a-million to suggest diet over drugs. Be very grateful. The doctor must realize how few patients' mood problems are actually effectively managed through medication. Most doctors take it for granted that patients will have to try many different drugs (with potentially terrible side-effects) before finding something that provides any relief. It's an utterly hit-or-miss operation. The actual mechanisms of the drugs are fuzzy at best, even to researchers. Your mom isn't suffering from a lack of Lamictal. It's something else.
To address your question more specifically - I have indeed heard of O-3 supplementation suggested for mood-stabilization. It did not work on its own for me. I do currently take it daily, primarily to avoid joint pain/inflammation that I notice when my O-6 intake is high.
I hope your mother finds relief. Good luck!