No, they each have their special housing. Though years ago both used the same, which is still used for brake cables. Indexed shifting requires special low-compression housing. BMX brake cables will probably work on a road bike, though I'm not sure if the BMX cable might be a bit thicker. If it fits through your housing and operates properly, it should be fine.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72