Lisp's evaluation strategy is based on a very particular category of rewriting systems known as the lambda calculus. Mathematica's is an abstract rewrite system with a broad set of evaluation strategies that are not easily represented in the lambda calculus (without first implementing a term rewriting system).

The syntactical building blocks might be similar but the execution model differs. While you could obviously achieve any sort of term evaluation with a metainterpreter, the TRS in Mathematica offers a rather smart rewriting system.

It can easily express things like associative and commutative operators (esp. useful if you have a pattern that matches on a use of that operator), and alternate evaluation orders (outside-in, mixed, lazy, held, &c). These are hard to trivially implement w/o very different kind of interpreter.

In this sense, most Lisp implementations pick a static evaluation strategy and leave implementing alternatives to a metainterpreter, which isn't exactly what's happening in Mathematica.