Kelvin did not merely believe that vitalism warranted serious scientific consideration, he thought it to be "absolutely forced by science". In less strong terms, it was a popular idea at the time, given the state of both physics and biology. There was also interest in reconciling physics with free will, etc. Helmholtz, Maxwell, and Boltzmann, among others, were sympathetic. The idea remained respectable even in the early 20th century, Bergson's Creative Evolution (1907) was quite influential.
Kelvin was a devout Christian, an elder in the Church of Scotland and the Chairman of the Christian Evidence Society in London, see Kelvin, Humble Christian. He advocated divine "creative power" in nature as attested to by science in various addresses for over 30 years. E.g. in the Chairman's address from 1889 we read:
"I have long felt that there was a general impression in the non-scientific world [that] believes Science has discovered ways of explaining all the facts of nature without adopting any definite belief in a Creator. I have never doubted that impression was utterly groundless. It seems to me that when a scientific man says – as it has been said from time to time – that there is no God, he does not express his own ideas clearly. He is, perhaps, struggling with difficulties; but when he says that he does not believe in a creative power I am convinced he does not faithfully express what is in his mind. He is out of this depth…"
While he admitted evolution, it was to be reconciled with God's creative power. "We must pause, face to face with the mystery and miracle of the creation of living creatures", he said in 1897. After a course of lectures on Christian Apologetics, given by Henslow to the Christian Association of the University College, Kelvin made public remarks that linked his creationism to the vital principle by name. Kelvin's arguments, I am afraid, were neither original nor very developed. The version of the report in The Times on May 2, 1903 edited by Kelvin himself, reads:
"I am in thorough sympathy with Professor Henslow in the fundamentals of his lecture. I do not say that, with regard to the origin of life, science neither affirms nor denies creative power. Science positively affirms creative power. Science makes every one feel a miracle in himself. It is not in dead matter that we live and move and have our being, but in the creating and directive Power which science compels us to accept as an article of belief. We cannot escape from that conclusion when we study the physics and dynamics of living and dead matter all around. Modern biologists are coming once more to a firm acceptance of something beyond mere gravitational, chemical, and physical forces; and that unknown thing is a vital principle.
We have an unknown object put before us in science. In thinking of that object we are all agnostics. We only know God in His works, but we are absolutely forced by science to admit and to believe with absolute confidence in a Directive Power in an influence other than physical, or dynamical, or electrical forces. Cicero, editor of Lucretius, denied that men and plants and animals could have come into existence by a fortuitous concourse of atoms. There is nothing between absolute scientific belief in Creative Power and the acceptance of the theory of a fortuitous concourse of atoms. Just think of a number of atoms falling together of their own accord and making a crystal, a sprig of moss, a microbe, a living animal."