[Tex/LaTex] Substituting character $l$ with $\ell$ throughout math mode

Question

How do I overwrite the default $l$ character so that it is substituted by $\ell$ throughout math mode?
(More generally, is there an easy way to make such symbol substitutions?)

Answer 1

This is similar to how MinionPro deals with open vs closed mathematical g's.

\documentclass{article}
\mathcode`l="8000
\begingroup
\makeatletter
\lccode`\~=`\l
\DeclareMathSymbol{\lsb@l}{\mathalpha}{letters}{`l}
\lowercase{\gdef~{\ifnum\the\mathgroup=\m@ne \ell \else \lsb@l \fi}}%
\endgroup
\begin{document}
\( l = 2 \) \( \lim = 2 \)
\end{document}