You are mixing up concepts. The Lisp concept of "the program is data" has little to do with modifying the program at runtime. It might be used for that in uncommon cases, but it is not recommended. A Lisp program usually is compiled into a static executable with a strict separation of data and executable code.

The mixing between program and data happens at build time in the compiler through the macro facilities. The first important thing is, that a Lisp compiler is not something which runs as an abstract process, but runs in a Lisp system and can execute arbitrary Lisp code. So Lisp macros can execute any Lisp functions - written by the user - to transform the input code, represented as data which can be easily processed, into the output code, which gets compiled. The whole point is, that with macro expansion you are not tied to some pattern language, but can run any user-written code to process the code for output. This gives Lisp great power and extensibility. But this happens at compile-time, not at run-time.

A good example of the power of this is, that the Common Lisp Object System (CLOS) can be entirely implemented in Common Lisp. You take any Common Lisp implementation which doesn't have an object system and load the CLOS code and you have the object system available.