It is impossible to say for sure what is wrong without a veterinary examination. However, the fact that your dog is not putting weight on her back paw but allows you to touch it suggests a few possibilities:
Possible Causes
Soft tissue injury: Sprain, strain, or muscle tear.
Bone injury: Fracture or dislocation.
Inflammation: Arthritis or tendonitis.
Neurological problem: Nerve issue or spinal injury causing weakness or paralysis.
Why Your Dog Might Let You Touch the Paw
Dogs have different pain thresholds. Your lab might not be in excruciating pain, or she may be used to being touched. She may also not associate the pain with the paw itself.
What to Do
It is crucial to schedule an appointment with your veterinarian as soon as possible. They can examine your dog, perform diagnostic tests such as X-rays, and determine the cause of the lameness.
In the meantime, avoid:
Putting weight on the affected leg—this can worsen the injury.
Giving medication without your veterinarian's approval.
Only a veterinarian can properly diagnose and treat your dog's condition.