When I attempt to use any kind of "long" arrow in the Lucida Bright font, it ends up coming out broken. For a MWE Consider the following:
\documentclass[10 pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmainfont{Lucida Bright OT}
\setsansfont{Lucida Sans OT}
\setmonofont{Lucida Sans Typewriter OT}
\setmathfont{Lucida Bright Math OT}
\begin{document}
Here is an example of an arrow which looks weird:
\begin{gather}
\widehat{\mathcal{O}_v}\otimes_{\mathcal{O}_v} k\xrightarrow{\approx}\widehat{k}
\end{gather}
here is another example:
\begin{gather}
\varprojlim k[T]/(T^n)
\end{gather}
\end{document}