A dog can be given some aspirin for a limp if the limping in the dog is caused by inflammation or other pain in the leg or foot.
The aspirin can help with the inflammation and pain and help the limping.
If the the limping is caused by something else then the aspirin may not work depending on what is causing the limping in the dog.
Sometimes the limping may be simply caused by the dog having something stuck in it's paw such as a sticker or thorn etc.
So check the paw to ensure nothing is in the paw and causing the limp.
Your dog may also have a sprained leg or other issue with it's leg that is causing the limp so if the limping continues you should take the dog to the vet if possible to have them checked out.
You can crush an aspirin up and mix it with the dogs food so that makes it an easier way for them to take the aspirin.