Homoiconicity is part of the answer. The other part is that Lisp is built up from a small number of axioms (probably the smallest such number) that are Turing-complete and at the same time are a language that people would actually want to use.
As pg says: "In 1960, John McCarthy published a remarkable paper in which he did for programming something like what Euclid did for geometry. He showed how, given a handful of simple operators and a notation for functions, you can build a whole programming language. [...] It's worth understanding what McCarthy discovered [my emphasis], not just as a landmark in the history of computers, but as a model for what programming is tending to become in our own time. " http://www.paulgraham.com/rootsoflisp.html
Why does pg say McCarthy discovered Lisp, not invented it? I think because it's something of such simplicity that one can imagine others inventing the same thing. So if humans contacted intelligent aliens, it wouldn't surprise me if they had independently invented Lisp, just as it wouldn't surprise me if they'd invented prime numbers, or cartesian co-ordinates.
As pg says: "In 1960, John McCarthy published a remarkable paper in which he did for programming something like what Euclid did for geometry. He showed how, given a handful of simple operators and a notation for functions, you can build a whole programming language. [...] It's worth understanding what McCarthy discovered [my emphasis], not just as a landmark in the history of computers, but as a model for what programming is tending to become in our own time. " http://www.paulgraham.com/rootsoflisp.html
Why does pg say McCarthy discovered Lisp, not invented it? I think because it's something of such simplicity that one can imagine others inventing the same thing. So if humans contacted intelligent aliens, it wouldn't surprise me if they had independently invented Lisp, just as it wouldn't surprise me if they'd invented prime numbers, or cartesian co-ordinates.