Uhh..... I wouldn't use that. I don't actually know if it will hurt anything or not, however small the damage may be (I'm guessing not at all!), but I would not use that when you could use chemical fungicides that are widely used and known safe. I'm sure they work better than dish soap and lavender oil anyway. It's sort of like making your own toothpaste. You CAN, but why bother when it doesn't have the chemical goodness and cavity fighting power? We live in the 21st century; we should take advantage of the horticultural advancements.
If you're into the environment, and don't want to use chemicals (although dish soap has chemicals in it, unless it's some homeopathic crap) then I suggest using cinnamon, or neem oil, or both! You can also make a cinnamon extract.
Dump some cinnamon in a jar of RO water, mix thoroughly so that none is dry (it's a bit hydrophobic).
Put it in the microwave and bring to a boil. You're house will smell like fresh Cinnabons. Take it out and stir, or my preference, put a lid on it and shake shake shake!
Let it sit for about 15 minutes. There will be a sticky mass that floats to the top. Skim this off and discard. Once you have done that, let the remaining liquid sit until sediment collects in the bottom. Decant the liquid, and voila! Add about a teaspoon of bleach, but ONLY if you're going to use this on pots alone. Don't apply it to the plants. Of course, adding bleach would negate the purpose of using all natural products.... Bleach will change the color of the liquid from a milky light brown to a dark clear brown.
Or just sprinkle cinnamon liberally over your plants. It won't hurt them. Go ahead and sprinkle cayenne pepper over them (and especially the soil) liberally if you have squirrel problems. Liberally does not mean dump it on, by the way! I still highly suggest skipping the "home remedies" (except for cayenne pepper and squirrels. It really works! I wonder if pepper spray would be a more convenient method?) and buying chemical fungicides, or at least a commercially available fungicide containing neem oil. I like Schultz's 3 way fungicide/insecticide/ miticide. It has worked for me every time I have used it, with one exception where I had to buy something more heavy-duty (I can't remember what it was, but it was so thick that the spray bottle it came in would not spray properly. It was almost the consistency of pudding and I had to dilute it with water to work with it)
OR you could do what everyone else does, and use chemicals! The best offense to fungi is a good defense, however! Plenty of light, air circulation, and regular pruning of dead plant material will not only give you nicer plants, but reduce the risk of fungi! A GREAT natural (sort of, it's been bred by man) product is Trichoderma! I love the stuff! Don't use fungicide if you use Trichoderma (or at least don't let any get in the media) and Trichoderma is a fungus. I think everyone should use this stuff, as it's also hypothesized to help the plants uptake more nutrients via their roots. I've never done any actual experiments, however. It definitely does no harm.
I looked at your posts to try and find out where you are. Atlanta! Perfect. I see that you have a chronic problem with root fungi. That's very unusual, especially during spring and summer. That is not good at all. Remove all of the plants (now would be a PERFECT time since they haven't started actively growing yet), wash them off, including the roots and rhizomes with RO water, remove any dead tissue and only pieces of rotting petiole still attached to the rhizome, remove any dead rhizome, and spray liberally with fungicide (I suggest neem oil, I'll say why later). Throw away the media and the old container. In another post you say your media is 2/3rds sand, 1/3rd peat. While 2/1 sand/peat works great for me, I don't have the root issues you do. Try something like 1/1/1 sand/peat/perlite and see if the extra air circulation doesn't help. Don't used an undrained container, the plant's don't need it. If it's inconvenient to water everyday (especially with the drought we've been in GA for the past 5 or 6 years) the put them in a half inch of water. Let the water evaporate, and wait one or two days before refilling (unless the heat is very bad). Spray the plants according to the instructions for a week or two. Six months later, when the neem oil should have dissipated and broken down, inoculate the media with Trichoderma if you wish.
Seems like a lot of trouble, but you said you have had chronic root problems, so that's my advice. And by the way, I hope you, your plants, and your cat are OK. I couldn't believe the hurricane. It was like a movie.