Let's analyze the sentence:
* Dog: Noun (subject of the sentence)
* lives: Verb (present tense)
* at: Preposition
* ranch: Noun (object of the preposition)
If you were to add "that" to the sentence, it would be used as a demonstrative pronoun to point out a specific dog.
For example:
* That dog lives at the ranch.
In this case, "that" is used to identify a specific dog, likely one that the speaker and listener are both aware of.