Nope, Nick, if you're using the Harbour Bridge to head North out of the city towards Lane Cove, then you wouldn't normally have to pay the toll for the bridge, so you shouldn't have to pay it for the taxi either.
BUT, if you use the Harbour Tunnel instead of the Harbour Bridge, then IIRC the charge works both ways, but as Andrew says, off-peak is a pretty quick trip, either way. And it's best to ensure they DON'T use Victoria Road, as any money saved on the tolls you would have paid would not make up for the time you've lost.