I'm thinking of lying about my dog's age
Really? Why?
Because when I tell the truth, I might get in trouble with the vet when my dog has to be put down....
You should not lie to your vet. If your dog is healthy, your vet probably won't want to do it anyways.
But I love my dog a lot and don't want to see her go.
If the dog is healthy, a vet will not put her down due to age.  If the dog has a low quality of life, then it is time to make a decision that is best for the dog, but a vet will not euthanize them against your will.