John McCarthy is not the one who implemented LISP 1 in IBM 704, but it is Steve Russell. McCarthy invented the idea of LISP in 1958 https://www-cs.stanford.edu/memoriam/professor-john-mccarthy that is before the 1960 paper and the LISP 1 manual. In the 1960 paper, he showed that LISP can be implemented in just few primitives that showed its purity of LISP. Of course you can develop a non pure version of LISP which is more practical.