After looking for a builtin expectation symbol in LaTeX, and coming up with none, I’ve defined one. Just add:
% Expectation symbol
\DeclareMathOperator*{\E}{\mathbb{E}}
to your LaTeX preamble and you’re done. You’ll also need to add \usepackage{amsmath} or in LyX to tick “Use AMS math package” under Document->Settings->Math Options.
Using the starred version of \DeclareMathOperator makes sure subscripts goes beneath the symbol in display mode.

Thanks for the tip. You need to import
\usepackage{amssymb}in order for this to work.