How to obtain a lowercase cursive “o”?

This is a lowercase “o” in a script alphabet; the best approximation I can offer is via the mathalfa package:

\documentclass{article}

\usepackage[scr=boondox]{mathalfa}

\begin{document}

$\mathscr{o}$

\end{document}

@egreg's solution is as close as one is going to get to the symbol you displayed, but here's an alternative.

\documentclass{article}

\usepackage{dutchcal}

\begin{document}

$\mathcal{abcdefghijklmnopqrstuvwxyz}$

\end{document}