Has there been a lexer that takes in much more than a regular language? I understand the restrictions, because a regular language is expressive enough to allow all types of tokens. And even if some context is needed in many languages to tokenize properly, they all seem to be "approximately" regular languages.

Yet I would be interested if any attempt in any programming language, possibly esoteric language, has been taken to completely eschew the conventional division between type-3 lexers and type-2 parser.
FORTRAN is famous for having some difficult to lex constructs, but those difficulties result probably more from having been designed before the classification was established (or at least known in programming circles)
Several languages are described with a type-3 lexers but some characteristic are easier to handle by feeding information from the parser to the lexer (C/C++ typedef, C++ templates, Ada/VHDL attributes)
Several languages have layout rules (Python, Haskell) which are usually not described as type-3 lexers (I don't know if it is possible to do so or not)