I'm having no luck with this project.

This is a bathroom with a light controlled by a switch. It also has an
outlet by the sink, and both the light and the outlet are on the same
circuit. The switch turns off both the outlet and the light.
Everything worked just fine with a regular outlet, but now the lights
won't turn on or off with the GFCI outlet in place. The outlet has
power, but the lights don't, and I can't figure out why.

There are two lines feeding into the outlet box, one the load line,
and the other to the light, I believe. I've wired it the same way as
the original outlet, but no joy. Is a GFCI not possible in this
situation?