Dr. Edward Feser continues to do the heavy lifting here: edwardfeser.blogspot.com/2012/10/is-god-of-classical-theism-dead.html
Aquinas himself considers the question of whether God can be said to have life, and answers:Life is in the highest degree properly in God. In proof of which it must be considered that since a thing is said to live in so far as it operates of itself and not as moved by another, the more perfectly this power is found in anything, the more perfect is the life of that thing.He then goes on to argue that intelligent beings have a more perfect kind of life than non-intelligent living things have, since the former operate of themselves, or independently of other things, to a greater degree than the latter. With that much the theistic personalist would presumably agree. But then Aquinas argues further thatthat being whose act of understanding is its very nature, and which, in what it naturally possesses, is not determined by another, must have life in the most perfect degree. Such is God; and hence in Him principally is life. From this the Philosopher concludes (Metaph. xii, 51), after showing God to be intelligent, that God has life most perfect and eternal, since His intellect is most perfect and always in act. [Emphasis added]In other words, precisely because God just is His act of understanding, which just is pure actuality, His intellect is maximally independent of other things, and it is this which entails that He has life to the most perfect degree. For since His intellect is, as it were, “always already” fully actualized it cannot be actualized by anything else, and thus cannot depend on anything else. That is to say, the doctrines of divine simplicity and immutability, decried as implying a “lifeless” God, in fact entail the opposite conclusion.