I don't have experience with this with my dachshund but my other dog, a 2 year old Schnoodle, did test from the doctors words, "slightly positive" for Lyme and to me she had shown no symptoms of it that I would have been able to look at and say yep she has Lyme. So her infection just happened to be caught on a routine wellness exam. From what it sounds like I had caught hers pretty early. Instead of putting me on the more expensive Doxycycline they prescribed Amoxicillin. It really did not seem to cause her too much grief to take the antibiotics, it was generally give twice a day with food for 1 month. For the most part taking antibiotics can likely cause stomach upset so should probably be given with some type of food or if the dog is having reactions to the medication it often can be resolved with lowering dosage or switching to another type of antibiotic. Just an additional fact, antibiotics are non discriminatory they "kill" any bacteria within the body even the good guys like the ones that exists in the intestinal tract so I would advise a good course of probiotics most likely after the full course of treatment is over so as not to interfere with the work the antibiotics are supposed to do. Giving probiotic and antibiotics at the same time or too close together can cause each to have very little to no effect at all. Anyway back on topic, the hope with giving antibotics if I'm not mistaken is to attempt to reduce the amount of Lyme antibodies to the point where they are less likely to "grow" and therefore cause more symptoms of the disease. Some dogs that are treated with months or even years of doxycycline still show positive antibody levels in the future so the antibiotic treatment is not a cure all. Despite treatment, the infection can "hide" out in the body for years and always has the potential to cause future problems. However, from what I've researched it seems that they are finding that treatment with antibiotics, especially closer to the time of infection, may lower the antibody levels faster than they would fall without treatment. It is thought that by lowering the antibody level it may reduce the risk of developing worse symptoms in the future.
It is true that many dogs can be asymptomatic. I think really the only thing I have noticed since my pups diagnosis is that at certain points one of Lady's back legs seems to crack when she sits which can indicate some kind of arthritis which can present as a symptom. She doesn't seemed to pained by it when it happens. She has not been officially diagnosed with arthritis by a vet so this is just my assumption, but rolling with that assumption I've started being more vigilant in giving her Glucosamine supplementation and making sure she's on a really good diet which I feed her raw or freeze dried raw, exclusively. I also try to keep on top of giving her oils which are high in Omega 3's and Omega 6 fatty acids which are thought to help decrease inflammation in the body. The important thing to know is that while Lyme is serious it can be present in a dog and not cause too much issue where unlike us humans we get hit pretty hard. From my research it seems that what we are classically familiar with as symptoms of Lyme in humans: Neurological disease (behavioral changes, seizures) and heart complications is rare in dogs.
If it were my pup I would go forward with the treatment but realize it is not a cure it is a hopeful band aide at best to attempt to reduce the likelihood that your pet will present with any worsening symptoms if they have any or continue to not present any symptoms as if they were not infected with Lyme at all. I have not had Lady retested since her course of antibiotics to find out if she is still showing signs of Lyme antibodies but I don't see that she is having much difficulty in her daily life at this point so I'm pretty comfortable at this time that she is okay but will make sure that when I go to my new vet that they know she was tested as Lyme positive by her former vet so that they can keep an eye on it. I did also research whether or not the Lyme positive dog should still get Lyme vaccines and while there is some debate the general suggestion is yes that vaccination of healthy Lyme positive dogs likely should occur to try to lower the risk of additional future infections. Vet studies of the Lyme bacteria apparently are suggesting that one exposure to the infection does not necessarily mean immunity against another so vaccination is hoped to help with boosting immunity.
I also would most certainly look to trying to contain the problem as best as possible since you are in a high risk type situation with woods, bushes and deer and the like and make sure any grasses that you have control over are trimmed as ticks like to hide within tall grasses, though it is possible they can just be carried into areas your dog has access to by other animals wild or domestic. Ensure your pups are wearing some kind of tick preventative when they will be outside romping around and also make it a habit of checking them when they come in for any uninvited guests. It is generally thought that a tick can safely be removed and a reduced risk of Lyme infection if it is caught within 18 hours but be sure that if you are removing a tick from your pups that you do not squish the head as it can cause the tick to release the bad stuff into your pup which can lead to them being infected. If you're not comfortable with removing it yourself taking your dog to a vet to remove it is a good choice and often they can take you as a walk in and just do the dirty work for you.
Good Luck with your pups, it's definitely a scary diagnosis but I think with doing the suggested treatment and in my opinion supplementation (diet, essential oils, etc) you can attempt to help the symptoms of the disease from progressing too far and possibly affect the quality of life of your darling pups
