You obviously aren't a Lisp "fanboy", because the boys and girls that fit that description can usually be relied upon to know that Lisp is a compiled language. Lisp appeared in 1958. The 1961-dated Lisp 1 manual already describes compiling.
Interpreting is useful; it gives us semantics without having to write a compiler first. This semantics provides a reference model for the compiled semantics: ideally, interpreted and compiled programs do the same thing. When we find they don't, we either resolve it, or somehow delineate and justify the situation.
Interpreting can be used to bootstrap a compiled Lisp system without requiring an existing Lisp implementation, but instead using another language such as C. Interpreting avoids the need to write a Lisp compiler in the bootstrapping language.
The CLISP implementation of ANSI Common Lisp is a good example of this. To build CLISP you need only a C compiler. CLISP's Lisp compiler is written in Lisp. So, of course, you have nothing to run that compiler with. The solution is to interpret the compiler using an interpreter written in C.
While running interpreted, the compiler compiles much of the Lisp library. The result of this is what CLISP calls a "half-compiled memory image": an image which contains compiled routines, but some interpreted routines. (I think, the compiler itself is still interpreted code).
This half-compiled image is then used to compile the remaining code, resulting in the fully compiled image.
Without the interpreter, CLISP's compiler could only be bootstrapped by insisting on another Lisp implementation to be installed first. (The way you need a C compiler to boostrap GCC). Or else, CLISP's compiler would have to be written in C, so that the compiler is compiled using the existing C compiler, and then applied to Lisp code to compile it before it can be run.
Nobody in their right mind wants to write a Lisp compiler in C, and requiring a Lisp implementation to build a Lisp implementation is a big disadvantage in a world in which Lisp isn't ubiquitous. What would happen under the Lisp-compiler-in-C boostrapping model is that the Lisp compiler written in C would be a completely minimal and possibly incomplete one that emits poor quality code, only good enough to initiate the boostrapping, and a "real" compiler would still be written in Lisp.