You've gotten a lot of great advice here. I've dealt with this problem a few times.
A few thoughts:
1. Is she under a doctors care, and if so, what does he feel needs to be done? If she's this sick, she is self diagnosing and this isn't a good idea to get too deeply involved in.
2Most of these deodorizers that cause this reaction are oily in nature, but invisible to the naked eye. You should use a prespray that breaks down oils, but that doesn't have a strong fragrance or VOC's. Its difficult to know if she is reacting to THAT perfume oil, or to any oily substance that has a smell. That's why "Step 1" is so important.
3. If you are comfortable doing so based on medical advice, use the strongest and lowest odor prespray you have access to, prespray and agitate the carpet (think of invisible restaurant grease), then hot water extract using a rotary jet extractor or high flow wand. She should not be in the home while you do this, as hot water will likely cause more of the odor to release into the air, such as it will with urine.
4. A truck mount is important to be used, or if you only have a portable, one strong enough to leave on the porch. Recirculating the odor from the lavender oil you pulled out of the carpet into the air will make her feel worse.
5
They may have used that product on other surfaces. They could have used the same product or fragrance in everything.
Good advice from Dave on this one. If that stuff is on walls, baseboards, vents, etc...she has a major problem.
6. And don't forget the best advice you were given above:
BTW are you collecting for a restorative type cleaning? Sometimes we feel obligated to offer endless cleaning attempts for free until the issue has become resolved. Just keep in mind you are there to help her with her problem.