Byron Bay is the most easterly point on Australia's mainland. There is certainly a lighthouse there, at Cape Byron. See the related link.
Historically, it has been. Nowadays, with devices such as GPS in use, not so much.
Cape Engaño Lighthouse was created in 1888.
Green Cape Lighthouse was created in 1883.
Cape Agulhas Lighthouse was created in 1848.
Cape Schanck Lighthouse was created in 1859.
Cape Bojeador Lighthouse was created in 1892.
Cape Liptrap Lighthouse was created in 1913.
Cape Melville Lighthouse was created in 1892.
Smoky Cape Lighthouse was created in 1891.
Cape Rachado Lighthouse was created in 1863.
The distance between the Cape Hatteras Lighthouse and the Cape Lookout Lighthouse is about 245 miles. Driving time would be approximately 5 hours and 16 minutes.