People often use lime when they plant, but it's best to hold off using it unless you know that the lawn needs it. If your soil already has a high pH, the lime can be harmful, raising the pH to a level that the grass won't tolerate. The real problem may be the heavy amount of traffic. Kids and dogs are hard on turf. A mature lawn might withstand them, but any lawn less than a year old won't stand up to extensive wear and tear. If possible, keep the dogs and kids off the lawn while it is still young. Planting your lawn in sections is one way to accomplish this. It also matters what steps you took when you planted the lawn. Starting right is half the battle when planting seed. Before you plant, make sure that the soil is loose. Water frequently so the grass seedlings never dry out in the first 4 - 6 weeks. Keep traffic off the seeded section of lawn as long as possible. (Maybe you could fence off half the yard and get grass growing there, then do the other half.) If you follow these steps, you should succeed and have a healthy lawn. Another alternative is sodding. It's more expensive, but it will give you an established lawn that tolerates foot traffic more quickly.