FFS, she's such a liar.
Strip lighting (fluorescent lighting to us non-Americans, Jack) can certainly trigger migraines if you're sensitive to them - particularly those at the end of their lives or with ancient and/or dodgy ballasts.
But where are you finding those today, Jack?
Maybe in a corner shop, I suppose - but most lighting is LED these days, and any remaining fluorescents in those "big stores" will use high-quality electronic ballasts that run at a high enough frequency that they can't possibly trigger photosensitive migraines.
And if she claims it's something to do with colour temperature then that's also a lie, since she uses a fancy daylight lamp for her supposed SAD - and that'll produce a much bluer light than anything you'd ever find in a shop.
(I get really bad photosensitive migraines... or, rather, got - I'm not sure if it's the move to LED lighting or simply me getting old, but I've not had one for about five years now)