I think lexing is unnecessary with some methods, e.g. parser combinators and (I think) Might’s “Parsing with Derivatives”. And there are other tactics, like the other commenter mentioned.
There are alternatives, certainly. And lisp style languages are especially easy to parse without a lexer. I was just taking issue to the term "quintessential" being used. In a classical sense, the lexer comes first.
It depends on your mental hierarchy doesn't it? It's easy enough to see lexing as a sub-step of parsing. It's also quite arguable that the classical emphasis of a separation between parsing and lexing is as much an artifact of classical tools than a "natural need".
For instance, from a Chomsky's hierarchy of languages perspective lexing and parsing are simply language analysis at two different levels on the hierarchy with lexing focused on the "regular" language embedded within a larger context-free or context-sensitive language.