I've got a lot of thyme in the herb garden. But I can't say if it has an impact or not on ticks. If you like to use your lawn, thyme can't be trod upon in the same manner. Depending on the size of your yard, you could try using dry ice traps.

People have suggested thyme along the property boundary, but most ticks live on mammals: deer, rodents, dogs. My experience with natural pest control is that something might "deter" a pest from wandering in, but if the pest is there, it will stay, despite the unpleasant environment. My understanding of the tick life cycle is that they live on mammals, so they are going to come into your yard with the mammal, when they are engorged, they will drop off whereever they are and look for another host without travelling too far.

Which is to say, I don't think replacing your lawn with thyme is going to solve your problem. Will it reduce it? Maybe. Some people use tick tubes --- mouse nesting material impregnate with tick killer that the mice take to their nests.

You might try Wondercide, which uses only safe plant products and is supposed to work against ticks.

I've never used it and have no financial interests in it. Just making a suggestion.