In many Lisps (+ + +) means this: call the function named + on the two values from the variables named +. The function is then a function object and the values of + can be anything they are currently set to.
Thus + serves more than one purpose: function or variable and both may be different values.
Thus the position actually matters.
What we have below the Lisp syntax are s-expressions: nested lists of symbols and other objects. In s-expressions, symbols need to be separated by whitespace, parentheses or possibly by some special character type (-> terminating character). Characters like +, -, /, *, _, ... are valid characters for any symbols.
Thus Lisp does not require functions to be separated by characters but symbols. That's a part of the reader mechanism for reading s-expressions (-> symbolic expression).
Infix has nothing to do with it. - refers to the subtraction function regardless of whether it is placed in prefix or infix position. Infix will trigger a type error, not a syntactic error — it will tell you that e.g. it cannot call a fixnum. Lisp quite ordinarily requires function names to be separated from their arguments by spaces, which is just a special case of the rule that atoms need to be separated by spaces. That’s all.