I'm not sure I have much to offer, but since it seems there haven't been a lot of responses on it, I'll throw my experience out there.
My 11 year old has been on the Biocidin drops for probably close to 8 months. She's been on them, not for her Lyme / co, but for a stubborn eye infection that she's had for over a year. I can say she's definitely herxed on it, but it's been pretty mild. But things were cropping up that she wasn't experiencing before, so we upped her detox.
I also noticed that of all of us, she got sick the least this winter, and when she did get sick, it was very mild. This, of course, is anecdotal, and may not be related, but I thought it was interesting.
My LLND is the one who turned us on this; she said it's a great thing to have. I've also read it's great for overall immune health and is superb against colds and flu.
Interestingly, our ophthalmologist, who's been treating my daughter's eye infection, has been so impressed with the results from the Biocidin, that she's now using it instead of antibiotics for many of her other patients and is seeing great results.
I definitely think it's something we'll always have on hand, even if it's not always for Lyme. It seems to be an overall beneficial product.