If your dog is licking his or or paw and is limping on that paw then the dog could have a wound on the paw.
The wound on the paw would cause the dog pain which would then lead to limping and also cause the dog to lick the paw to help it feel better and to help it heal.
The dog may also have a thorn or sticker in it's paw and is limping as a result and licking the area to try and get it out.
Although most commonly the dog would use it's teeth to pull out the thorn or sticker first but then could still have some pain and be limping as a result and be licking the paw to help heal the wound.
If your dog is licking it's paw and limping hold the dog down and take a look at it's paw to see if any injuries are present and if so you can add some hydrogen peroxide to the dogs injury to help it heal up.