The direct benefit of Lisp syntax is that everything is consistent. Arithmetic operators have the same syntax as regular functions. Because all Lisp code has a consistent structure, that makes it easy to do some really neat things. For example, it isn't hard to write a program that takes Lisp code as input and processes it in some way.
This is the reason why you see so many people write a toy Lisp interpreter. It's really easy to write code to evaluate Lisp code because all Lisp code has an identical structure.
As a Lisp programmer, this benefit emerges in the form of macros. Macros run at compile time, take some Lisp code as input, and spit out new Lisp code as output. The new lisp code is then substituted for the old one.You can think of macros as a very small user-defined compiler. These let you build all sorts of language constructs that you couldn't build in other programming languages. For example, you can add pattern matching to a Lisp with macros. The macro would take a list of patterns and corresponding expressions as input and spit out some code that checks for the patterns and runs the corresponding expressions if the pattern matches.