Rather than going low carb right off the bat, why not try a more balanced diet but at a decent deficit and see if that works for her? She'll need to track her food to make sure that she's really in a deficit (and ideally would weigh the food as well so that she can be certain how much she's actually taking it). She might not actually have an underactive thyroid; it could just be that she doesn't move much so she doesn't burn much.
In the end it comes down to calories in/calories out. The macro makeup of the deficit can make the deficit a bit easier to endure, but it's really all about the calories. The first step is to determine how many calories she needs to continue at her current state and then to determine a decent deficit for her. How hard is she willing to work? She could accomplish weight loss by tightening up her diet, making sure to be in a deficit, and adding in NEAT (non-exercise activity) like walking and just upping the general activity level.
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"Do you choose to simply know the path, or do you choose to walk it?"
Your body keeps an accurate journal regardless of what you write down...
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