One of the things I like about our interaction, frabjous, is that we're mostly both right

.
You are correct that the symbol you posted is what one would normally get when using \mathcal{L}.
I was correct in that when *I* used \mathcal{L} I got the other symbol (the one you said was more desirable). But.... check this out:
Code: Select all
\documentclass[12pt]{article}
\usepackage{eucal}
\begin{document}
$\mathcal{L}$
\end{document}
I realized that my default setup has eucal for the math stuff, hence our difference. I had forgotten; sorry bout that. The good news is that the original poster here doesn't have to look for a hard-to-find package. S/he already has it.
I'm posting a pdf of the eucal version of \mathcal{L}.