As mentioned in the question, Turing was central to defining algorithms and computability, thus he was one of the people that helped assemble the algorithmic lens. However, I think his biggest contribution was viewing science through the algorithmic lens and not just computation for the sake of computation.
During WW2 Turing used the idea of computation and electro-mechanical (as opposed to human) computers to help create the Turing–Welchman bombe and other tools and formal techniques for doing crypto-analysis. He started the transformation of cryptology, the art-form, to cryptography, the science, that Claude Shannon completed. Alan Turing viewed cryptology through algorithmic lenses.
In 1948, Turing followed his interested in the brain, to create the first learning artificial neural network. Unfortunately his manuscript was rejected by the director of the NPL and not published (until 1967). However, it predated both Hebbian learning (1949) and Rosenblatt's perceptrons (1957) that we typically associated with being the first neural networks. Turing foresaw the foundation of connectionism (still a huge paradigm in cognitive science) and computational neuroscience. Alan Turing viewed the brain through algorithmic lenses.
In 1950, Turing published his famous Computing machinery and intelligence and launched AI. This had a transformative effect on Psychology and Cognitive Science which continue to view the cognition as computation on internal representations. Alan Turing viewed the mind through algorithmic lenses.
Finally in 1952 (as @vzn mentioned) Turing published The Chemical Basis of Morphogenesis. This has become his most cited work. In it, he asked (and started to answer) the question: how does a spherically symmetric embryo develop into a non-spherically symmetric organism under the action of symmetry-preserving chemical diffusion of morphogens? His approach in this paper was very physics-y, but some of the approach did have an air of TCS; His paper made rigorous qualitative statements (valid for various constants and parameters) instead of quantitative statements based on specific (in some fields: potentially impossible to measure) constants and parameters. Shortly before his death, he was continuing this study by working on the basic ideas of what was to become artificial life simulations, and a more discrete and non-differential-equation treatment of biology. In a blog post I speculate on how he would develop biology if he had more time. Alan Turing started to view biology through algorithmic lenses.
I think Turing's greatest (and often ignored) contribution to computer science was showing that we can glean great insight by viewing science through the algorithmic lens. I can only hope that we honour his genious by continuing his work.