This is called “proof by example” and is a fallacy.

Show me how to write `a + b * c` in Lisp without parentheses.

One version would be to actually leave the expression as is and temporarily switch the Lisp reader to Infix.

I'm loading an infix reader macro into LispWorks, the code is roughly 30 years old:

    CL-USER 1 > (ql:quickload "INFIX")
    To load "infix":
      Load 1 ASDF system:
        infix
    ; Loading "infix"

    ;;; *************************************************************************
    ;;;   Infix notation for Common Lisp.
    ;;;   Version 1.3  28-JUN-96.
    ;;;   Written by Mark Kantrowitz, CMU School of Computer Science.
    ;;;   Copyright (c) 1993-95. All rights reserved.
    ;;;   May be freely redistributed, provided this notice is left intact.
    ;;;   This software is made available AS IS, without any warranty.
    ;;; *************************************************************************

    ("INFIX")

Now we can write Infix expressions:

    CL-USER 2 > '#I( a + b * c )
    (+ A (* B C))

Let's set the variables a, b, c

    CL-USER 3 > setf a 10 b 20 c 30
    30

The Infix expression reader macro at work:

    CL-USER 4 > #I( a + b * c)
    610

Inside the Infix macro Lisp parses a sublanguage of Infix expressions into Lisp s-expressions. Generally this would be possible with a normal macro, but the reader also changes the tokenizing of elements, so we can also write:

    CL-USER 5 > #I(a+b*c)
    610

In "normal" Lisp syntax a+b*c would be a single symbol. The infix reader parses it into five symbols and a list according to operator priorities.