first task is to select the appropriate tool, namely the
only brush-based tool in Lightroom (2.0+),
the healing brush. It is to be found on the right in the
upper icon row of Develop window.
You don’t have to rummage through the piles of sliders,
just select Effect menu and within that
click on Iris Enhance. This is a preset
designed especially for brightening the eyes, the iris.
Beside brightness it also enhances saturation and clarity/contrast.