If she is on clonazepam, do not think you can replace it right off with any non-prescription substance. It's my opinion the elderly should not be on benzos (in general for the generally healthy), but once on them long term, they'll have withdrawal symptoms if taken off suddenly. They should be weaned very, very slowly. And even more slowly than that. If they've been on them many years and if it's anything other than a tiny dose, it might not be worth it to try to get them off of it. They'll suffer too much.
In general supplements are milder and safer than prescription drugs. Which makes sense - that's why they're not regulated. Prescription drugs are concentrations that act like a sledgehammer. Supplements generally have a more nuanced, gentle, subtle effect. They usually cannot replace a prescription drug outright - by that I mean suddenly overnight. But they can affect the same neurotransmitters and so can stack, so I would be very careful taking supplements along with prescription pills. Which is basically what Cap'n Jack said.
All drugs that have a psychoactive effect, in my opinion, create a dependency that when withdrawn cause great discomfort. I'm having this issue with my 90 year old mother and her Exelon patch. they switched her to generic and it must have been weaker or something, she could not handle it. We had to get her doctor to order the brand, and she is paying $90 more a month for it because the insurance won't cover the total cost. We have to make sure she does not run out, if she goes a couple days without it, she gets very confused and depressed.
You don't say what your goal is with your mom, is it to replace clonazepam with lavender oil? Is she finding that the clonazepam is no longer helping as much with her anxiety? This is tolerance and is the main reason it's just a bad idea to stay on benzos as a long term treatment for anxiety.