Sooooo, I think that lavender and cedar and cloth bags work okay when you are just trying to discourage any stray, random moths from eating your wool. I think you'll be fine, Thistle.
I (woe) am tortured by a moth infestation. I bought an old house that I didn't know had a moth problem and I never thought to fumigate it before moving in. I carelessly exposed my wool carpets, wool coats and wool and cashmere sweaters to them. I provided them an endless bountiful feast in the form of my knitting yarn. They decimated my wools. And they come back every year! So, I've read a lot, experimented a lot, and found a few things to be true.
1. Always fumigate your home before moving into it and NEVER trust an antique dresser to be moth free.
2. Lavender and cedar are deterrents. Hungry moths will get past them. I've seen a moth land on my bottle of lavender oil.
3. Chemical moth balls smell awful, but work.
4. Getting the chemical moth ball smell out of things takes foreeeeeever. It is there after washing; it is even there after dry cleaning.
5. Washing wool deters moths because it cleans off the oils/food particles that we can't see, but they love to munch.
6. Washing does not destroy moth eggs. You need to heat your dry wool by putting it in the dryer for a long time to destroy the moth eggs.
7. Dry cleaning removes the oils/food particles and moth eggs. Dry cleaning is 100%.
8. However, neither washing nor dry cleaning will keep a moth larva from trying to eat your sweater if it is hungry enough, so the sweater has to be protected after cleaning.
9. Nothing works better for storing your wools than one of those extra big ziplock bags you can buy. Nothing. Moths can get through zippers and holes in cloth storage bags. (You can imagine how I know.) They can't get through the ziplocks. The bags don't breathe though, so be sure to store them in a cool, low temperature change environment. Add silica gel sachets if you can to take out any humidity trapped in the bag. And it goes without saying that you shouldn't store things for years and years in them without airing them out.
So, there you go. My words of advice. The words of a woman who has suffered much at the hands (wings?) of moths. (Shaking fist in air!)
ETA: I just realized that I didn't say exactly what I do to prepare and store mine. I dry clean everything that I cannot stand to lose. Straight from the dry cleaner it gets folded and put into the ziplock bag along with a few silica gel packets. Things I don't feel as strongly about (my knit hats, scarves and gloves mostly) get washed, are thoroughly air dried and, when absolutely bone dry, thrown into the dryer on high for an hour. However, I default to dry cleaning if in doubt about whether an item will be damaged by the dryer. Out of fear, I split things between multiple bags and I never mix hand washed with dry cleaned. I haven't lost anything to moths yet with this process, but every year I am anxious. Those beasties are horrible!
