When compiling the AST sits in the middle of the whole process. The first part deals with parsing your language into the AST the second part deals with transforming the AST to the target language (including possible optimizations of the tree).
Lisp is effectively the raw AST, which is where its power comes from. The use of parentheses is the cleanest way to directly represent a raw tree that you can interact with. This means that you can use Lisp to cut the language design process in half from either direction:
On the one hand, if you are worried about parsing your language, then you can simply transform it into lisp, which is virtually identical to creating the AST, and then you can use a lisp interpreter/compiler for the second half.
On the other hand, if you're interested in writing the interpreter/compiler for a language and don't want to stress about parsing, you can write it for lisp and not have to worry about parsing a complex language. If you follow the Norvig code you can extend that example to a language devoid of parenthesis by writing the parser for it.
Even if you want to do both it's not a terrible idea to prototype both halves using Lisp and then perform the minimal work pull out the Lisp code and replace it with some other implementation of the AST.