If the dog is just limping after walking it could be that the dogs leg is tired or the dog may have gotten something such as a thorn or even a small piece of glass etc in it's paw.
So check the dogs paw to see if something got into the dogs paw.
Sometimes after a long walk my dog will limp on one leg for awhile and then switch to limping on the other leg and the vet said that it was probably just because the dog has tired it's legs out.
Just like humans after walking or running for awhile our legs and even feet can start hurting.
It could also be that the dogs paw could sore from all the walking as well.
Other things that can cause a dog to start limping after walking are Injuries, broken bones, fractures, sprains, dislocations, ligament tears, joint trauma, and spinal injuries.
If the dog continues limping after a few days then I would take the dog to the vet to get checked out.
However most times it is nothing to worry about and the dog could have just sprained their ankle as well or sprained their foot.