I’m not sure that I would change it. You’ll have to pull some of that turf up and cut it in order to put a thicker border like stone. You’ll likely have to retamp the base for the turf, stretch and nail it, and brush in more infill. That’s if everything was done correctly from the original install.
She definitely want clean lines. No curved border. Desires rectangular stones that do not have to be exact match.I would do river rock, the 3-5” size. A random placed “triple row” type effect could likely be installed right over top of the existing edging or you might need to pound the edging a bit lower. Should be an easy install.
Unfortunately, given the formality of the existing hard angles and straight lines, it’s possible that when your customer says she wants “stone border,” she means rectangular stone Belgian blocks or something equivalently formal installed as inset into the bed. Any chance she would clarify what she wants?