Fellow chronic Lyme patient here.

I was given 2 rounds of doxycycline which seemed to do absolutely nothing.

1. Doxy is not the worst antibiotic for targeting lyme that's got into the central nervous system, but from personal experience and the doctors that have treated me, it seems Minocycline is preferable. Note that it may seem like you're having a bad reaction to the medication, but this is probably just the Jarisch–Herxheimer reaction. I was told to gradually increase the daily dose to make it more bearable.

2. Once the infection gets to the chronic stages, a single type of antibiotic will at best suppress the infection, it will normally not get you anywhere near a cure. Different doctors will have different go-to combos, but should generally be flexible about it and try different combos if one isn't really working. Again, this should also be influenced by the affected organs based on symptoms. I'm glad you're now getting such a combo, many doctors who don't specialise in Lyme disease will not prescribe that kind of thing even if there's now a decent body of literature that this does work in many cases.

I've been on 3 antibiotics (simultaneously) for the last 2 months and I feel so much better - not 100%, I'd say 85%.

I've been there - be prepared for this potentially being a long slog, depending on severity and affected organs. After first developing symptoms in 2013, I finally got a diagnosis in early 2015. (Backed up by positive test results - Lyme ELISPOT/LTT, the ELISA test shows nothing, apparently it's only about 40% accurate) At that stage I was pretty bad, I have almost no memories from late 2014. The doctor that first diagnosed me got me to a stage where I was symptom-free whenever I was taking antibiotics, but after 2-12 weeks symptoms would return.

I ended up switching doctor in late 2016 as my overall progress seemed to have stagnated. She turned out to be a lot more test-happy than the original guy, and tested for a whole range of other stuff - bacteria, fungal, parasite, viral infections and various other values related to inflammation, nutrition etc. She found that in addition to Lyme disease (2 different strains of Borrelia), my immune system was also in overdrive fighting a bunch of other stuff, which I got treatment for. Plus she switched me to a different antibiotic regime specifically targeting one of my main symptom areas (bladder/prostate). 2 1/2 years later I'm not 100% cured. One of the 2 Borrelia strains I was infected with seems to be gone. The other one is still lingering - I've just relapsed into a mild Lyme episode for the first time after 6 months of not taking anything, so I'm on another 3-antibiotic treatment cycle. The gaps are getting longer, and the symptoms are becoming less severe. My immune system still occasionally goes wild on fighting VZV too (chicken pox virus, once you've had chicken pox it stays in the nervous system) which presumably somehow gets an opportunity to flare up thanks to the Lyme bacteria doing their thing or my immune system generally being in a rough shape after years of infection.

One thing that seems to have helped me is doing regular intense exercise; I've taken up tennis, but anything that gets you properly sweating should do. The recommendation was actually to do regular infrared treatment, but I hated that, and intense exercise seems to work similarly well. The perspiration supposedly helps to get rid of the toxins from the bacteria (live or dying, see Jarisch-Herxheimer reaction) and the spirochete bacteria themselves apparently cope badly with a raised host body temperature. (An early treatment for syphilis, another spirochete, was apparently the high fever produced by contracting malaria. I don't recommend infecting yourself with malaria.) I have no idea how effective it is at those 2 claimed benefits, but it certainly seems to clear the brain fog for 2 days or so.

FWIW, no dietary modifications seem to have made any difference for me; the first doctor made me try a bunch of these but the change after a few months was just that I felt hungry a lot.