Yes, chickens do a nice job of eating ticks. We have woods that are full of ticks! As long as you check for ticks on you and the kids every night, Lyme disease should not be an issue. A tick carrying the disease must attack to you, burrow its head, and secrete the Lyme disease in the process of drinking your blood. This takes about 48-72 hours. We check our kids in the nude every single night. If we find a tick, we pull it off with a tweezers by the base of the skin. Sometimes we burn it off, but we don't like to do that on kids.
We use chicken tractors to keep chickens safe from predators, and lock in coop at night. Guinies are a better option if you are not looking for chickens. They are the better option for ticks, and are more "predator savy" my chickens often "play dead" when a predator is near, which gets them killed, guinies scream like there's no tomorrow.
Last but not least, soak clothes in promitherin I'm not sure i spelled that right. You can buy in bulk and dilute. We put it in 5 gal bucket, soak work clothes over night, wring out, line dry and wear. Tuck pant legs into long socks, and shirt into pants. Wear a bandana on head, and a hat over bandana. Soak bandana with clothes. Don't dump the promitherin in bucket when done. Put lid on and use again, or fill a sprayer and spray around house, or touch up clothing as needed...
Hope this helps you ;-) good luck!