Potted lavender seems to be dying off indoors
I have a 3 year-old 'Vera' Lavender plant (Lavandula angustifolia I believe is the proper name). It is potted, and since we occasionally have harsh winters here in Kansas City, I bring it indoors for the winter. In the past, this has not been much of a problem, because the plant was small enough to fit under supplemental grow lights, and I could limp it through the winter. This year, I don't have enough room to fit it under lights, so it is in an east-facing window that gets decent light in the mornings through the early afternoon. I acclimated the plant before I brought it indoors, and it seemed to adjust well for the first month and a half. As of the past couple of weeks, large canes have been dying off. My question is this: Will a lavender plant go dormant without full daylight/supplemental light, or is this something I should be worried about? I can include a picture, if that would help. Thanks for any and all advice!