Plants have the simplest soul for it drives them to grow. Animal souls possess that property plus the ability to act in some degree according to their own inclinations. However, it is the soul of man that has all those properties plus the ability to know God. That's what sets humanity apart.
Does that get Lexington into heaven? I don't know. Someone posted months ago since God wants you to be eternally happy with him in heaven, if having your beloved canine companion with you was intrinsic to that happiness, then God would certainly permit it.
Smiles.... Believe me... My current four-leggers in my house, 3 dogs and a cat, are each individual souls... They might not have the capacity to know God, but He knows them... And I think that is the key.