The notion is probably taken from Dante most immediately, but it's something which Lewis felt to be valuable in the mediaeval world-view in general. He describes it most completely in his The Discarded Image (1964) but it's also discussed in works as early as his essay "Dante's Similes" (read to the Oxford Dante Society on 31 October 1940, reprinted in Studies in Medieval and Renaissance Literature, CUP, 1966). The idea is that our mundane physics gives us a certain view of how the sizes and relationships of objects "work". However, in a spiritual sense, we can perceive things differently. The heavens are far away, but central in importance. They are above our heads but they are also "inwards" through being closer to God.
In Dante's Paradiso, the third part of the Divine Comedy, the poet ascends from Earth out through the heavenly spheres. This is in the version of cosmology where our world is in the centre and it is surrounded by larger and larger spheres, corresponding to the classical planets. The outer sphere, the Primum Mobile, gives the others their motive power; this is because it is impelled by God, who lives outside it in the Empyrean. Towards the end of the poem, as the poet crosses the last boundary, his perspective changes: he sees God not in the outermost part of the universe, but at its centre, surrounded by concentric rings of light. The Primum Mobile is now the innermost. The universe has been "turned inside out" (Discarded Image p116).
In Lewis's "Imagination and Thought in the Middle Ages" (two lectures in 1956, also collected in Studies op. cit.) he expands -
In our visible world the circumference, the Primum Mobile, moves quickest and is nearest to God; the Moon moves slowest and is nearest what we call the Centre - i.e., the Earth. But the true nature of the universe is exactly the opposite. In the visible and spatial order Earth is centre; in the dynamic, invisible order the Empyrean is centre, and we are indeed 'outside the city wall' at the end of all things. And the centre of that Centre, the centre of Earth, is the edge, the very point at which all being and reality finally peter out. For in there (as we call it), out there (as we ought to call it) is Hell - the last outpost, the rim, the place where being is nearest to not-being, where positive un-being (so to call it) asymptotically approaches that zero it can never quite reach. Such was the medieval cosmos.
In this world-vision, "further up" and "further in" are the same thing. They are both moving towards God. In the novel, we are moving not through an abstract space but a physical landscape, a "truer" version of Narnia (as Digory says, "it's all in Plato"). This again reflects spiritual journeys such as The Pilgrim's Progress (which Lewis explored in The Pilgrim's Regress, 1933), often illustrated as a path travelling both up the page, and into the landscape - towards the distant celestial city at the top. As the various characters of The Last Battle enthusiastically travel "further up and further in", they are responding to the divine message to go towards God. They are also leaving behind the "Shadow-Lands", a small and distant place far below, which is no longer important but which they used to consider to be the world.
The idea of being "outside the city wall", also discussed in The Discarded Image, is present in The Last Battle as what appears to be a walled garden turns out to be larger than (what we thought was) the entire world around it. The walled garden, or hortus conclusus, is also a standard mediaeval mystical image, generally standing for the Virgin Mary and her womb, a space which contained the incarnate God. In The Last Battle, Lucy transfers this imagery to the stable which "once had something inside it that was bigger than our whole world". But in any case, here too we have physical space yielding to a spiritual reality.
Some similar playing with physical and spiritual scale takes place in The Great Divorce (1945). The enormous grey town, which is either Hell or Purgatory depending on your perspective, is eventually seen to occupy only a tiny crack in the soil of Heaven. This book also bears the marks of Dante and Bunyan.
All of the above is Christian in the sense that it's rooted in a certain era of Christian experience, but it is not the sort of thing which is to be found explicitly in the Bible. It is a mystical, mythological, or poetic mode of expressing a Christian spiritual viewpoint.
