If you look at code with really low-level operators like CAR, CDR, CONS, ATOM, NULL, etc then this is the assembly level of Lisp. If you look at some Lisp Machines, which had a processor with a for Lisp optimized instruction set, many of those mapped relatively direct to corresponding machine instructions - using a mostly stack machine.

The CLISP implementation of Common Lisp has a virtual machine implementation.

Let's take some simple demonstration code:

    [1]> (defun foo (a)
            (car (cdr (if (null a)
                          '(1 2)
                          (cons 3 a)))))
    FOO

Now we compile it for the CLISP virtual machine:

    [2]> (compile 'foo)
    FOO ;
    NIL ;
    NIL

If we look at the disassembled virtual machine code, you'll see that the machine code has actually similar primitives for its stack machine:

    [3]> (disassemble 'foo)

    Disassembly of function FOO
    (CONST 0) = (1 2)
    (CONST 1) = 3
    1 required argument
    0 optional arguments
    No rest parameter
    No keyword parameters
    11 byte-code instructions:
    0     (LOAD&JMPIFNOT 1 L10)
    3     (CONST&PUSH 1)                      ; 3
    4     (LOAD 2)
    5     (CONS)
    6     L6
    6     (CDR)
    7     (CAR)
    8     (SKIP&RET 2)
    10    L10
    10    (CONST 0)                           ; (1 2)
    11    (JMP L6)
    NIL

Unrelated to that there is also the idea to program assembler code embedded in Lisp - this is often called LAP code (Lisp Assembler Program). Several implementations are using this.