No, you can't transmit it by kissing. Sexual transmission is up in the air. While there are stories of sexual transmission, there are lots of stories of no transmission even with years of no protection.
The official story is ticks-only, but I did read a case study of a shirtless guy who got bit multiple times on his shoulder and upper arm by a biting fly while jogging. He got several small bulls eye rashes, one at each bite location. Fortunately, his doctor was open minded enough to treat him based on the unique rash rather than the narrow belief that it only comes from ticks. (The Lyme bacteria has indeed been found in mosquitos and biting flies. The prevailing belief is that they don't transmit it to humans.)
Here's one thought about kissing... many people with Lyme can have their immune system suppressed. This can trigger re-activation of dormant viruses which can be transmitted via saliva, such as EBV and other oral viruses in the herpes family.
It's also likely that h. pylori is transmitted via saliva. It's believed babies get this bacteria by being kissed near the mouth or on the hands by family members. I am not medically trained, but if you want to be cautious, I would encourage you to keep your kisses for baby in places other than the hands or mouth.
Since Lyme bacteria are similar to those which cause syphilis, I would think a reasonable view is that both can be transmitted in the same fashion. And until that view is debunked, it would be a good rule of thumb to avoid inadvertent transmission.
It's so very frustrating that they have found the spirochetes in breast milk, semen, vaginal secretions, umbilical cord blood and yet they can't determine how/if it's transmitted from person to person!
Lyme and co's being transmitted sexually is highly debated. Some Dr's say yes and others say no. I wish I knew the answer too. I do not think it is transmitted from kissing. Otherwise, it would be a worse epidemic then it already is. My fiancée doesn't have it and we have been together 4 years and have not used condoms.