Catalan language "ela geminada"

You have several options available.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[catalan]{babel}
\usepackage{newunicodechar}
\newunicodechar{Ŀ}{\L.}
\newunicodechar{ŀ}{\l.}

\begin{document}
CE\Lgem A -- ce\lgem a

CE\L.LA -- ce\l.la

CE"LA -- ce"la

CEĿLA -- ceŀla

\end{document}

The last uses the Unicode characters (and requires UTF-8), the first three work in any input encoding.

Some time ago, one of my university colleagues gave me the following code to use the punt volat (Shift+3 on a spanish keyboard) as an active character. Sometimes I use it but I don't have it on any 'official' style file, then it's easier for me to use "l or \lgem{}.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[catalan]{babel}
\usepackage{lmodern}

%Definició de la ela geminada per tal que accepti el punt volat del teclat
\def·#1{%
  \ifmmode
    \cdot #1
    %\csname normal@char\string"\endcsname l%
  \else%
    \def\argument{#1}%
    \if\argument l%
      \leftllkern=0pt\rightllkern=0pt\raiselldim=0pt%
      \setbox0\hbox{l}\setbox1\hbox{l\/}\setbox2\hbox{.}%
      \advance\raiselldim by \the\fontdimen5\the\font
      \advance\raiselldim by -\ht2%
      \leftllkern=-.25\wd0%
      \advance\leftllkern by \wd1%
      \advance\leftllkern by -\wd0%
      \rightllkern=-.25\wd0%
      \advance\rightllkern by -\wd1%
      \advance\rightllkern by \wd0%
      \allowhyphens\discretionary{-}{l}%
      {\hbox{}\kern\leftllkern\raise\raiselldim\hbox{.}%
        \kern\rightllkern\hbox{l}}\allowhyphens%
    \else
      \if\argument L%
        \leftllkern=0pt\rightllkern=0pt\raiselldim=0pt%
        \setbox0\hbox{L}\setbox1\hbox{L\/}\setbox2\hbox{.}%
        \advance\raiselldim by .5\ht0%
        \advance\raiselldim by -.5\ht2%
        \leftllkern=-.125\wd0%
        \advance\leftllkern by \wd1%
        \advance\leftllkern by -\wd0%
        \rightllkern=-\wd0%
        \divide\rightllkern by 6%
        \advance\rightllkern by -\wd1%
        \advance\rightllkern by \wd0%
        \allowhyphens\discretionary{-}{L}%
        {\hbox{}\kern\leftllkern\raise\raiselldim\hbox{.}%
           \kern\rightllkern\hbox{L}}\allowhyphens%
      \else
        #1
      \fi
    \fi
  \fi
  }

\begin{document}
cel·la
CEL·LA
\end{document}

The result is:

An alternative solution, based on the previous one. Redefining directly · is not a good idea (problems with TOC, for example), and the proper way is redefining the LICR object \textperiodcentered. I even consider impossible cases, like l·L. I wrote it long ago and posted to the list es-tex (CervanTeX), and here I just copy and paste it:

\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage[catalan]{babel}

\def\xgem{%
   \ifmmode
 \csname normal@char\string"\endcsname l%
   \else
 \leftllkern=0pt\rightllkern=0pt\raiselldim=0pt
 \setbox0\hbox{l}\setbox1\hbox{l\/}\setbox2\hbox{.}%
 \advance\raiselldim by \the\fontdimen5\the\font
 \advance\raiselldim by -\ht2
 \leftllkern=-.25\wd0%
 \advance\leftllkern by \wd1
 \advance\leftllkern by -\wd0
 \rightllkern=-.25\wd0%
 \advance\rightllkern by -\wd1
 \advance\rightllkern by \wd0
 \allowhyphens\discretionary{-}{}%
 {\kern\leftllkern\raise\raiselldim\hbox{.}%
   \kern\rightllkern}\allowhyphens
   \fi
   }
\def\Xgem{%
   \ifmmode
 \csname normal@char\string"\endcsname L%
   \else
 \leftllkern=0pt\rightllkern=0pt\raiselldim=0pt
 \setbox0\hbox{L}\setbox1\hbox{L\/}\setbox2\hbox{.}%
 \advance\raiselldim by .5\ht0
 \advance\raiselldim by -.5\ht2
 \leftllkern=-.125\wd0%
 \advance\leftllkern by \wd1
 \advance\leftllkern by -\wd0
 \rightllkern=-\wd0%
 \divide\rightllkern by 6
 \advance\rightllkern by -\wd1
 \advance\rightllkern by \wd0
 \allowhyphens\discretionary{-}{}%
 {\kern\leftllkern\raise\raiselldim\hbox{.}%
   \kern\rightllkern}\allowhyphens
   \fi
   }

\newbox\LL\hbox{l·l L·l l·L L·L}

% No lo uso, pero es como podría guardarse el valor
% anterior:
\expandafter\let\expandafter\saveperiodcentered
   \csname T1\string\textperiodcentered \endcsname

% Y aquí está el quid. No hago nada con el argumento, pero
% se podría usar para, por ejemplo, considerar los 4 casos
% por separado:
\DeclareTextCommand{\textperiodcentered}{T1}[1]{%
   \ifnum\spacefactor=998
 \Xgem
   \else
 \xgem
   \fi#1}

\begin{document}

Por defecto:

\leavevmode\box\LL

\sfcode`L=998

Corregido:

l·l L·l l·L L·L

\end{document}