I don't think lining would be necessary. Coat the inside with a release agent (mineral oil, vaseline, etc.) prior to the pour. OR, simply place into a freezer for a short time, then remove.
If everything else fails, it's also not the end of the world to cut the pipe in half lengthwise, to get the soap out. Or, cut it apart beforehand, tape together, cast & let solidify, take off the adhesive strips, and disassemble.
Most of my recipes work well in unlined PVC pipes, as long as I freeze them for about an hour, then let them sit out for 5-10 minutes. The condensation works to lubricate the soap surface so the log slides out easily. Be sure not to fill the pipe all the way to the top; you want some space for the soap to more easily slide down the pipe and out of the mold.
I will say that my recipes are high in hard fats (lard, tallow, CO). The only time I've had trouble getting a soap out of a PVC mold was when I used a recipe higher in OO. Coincidence? Perhaps. It was one time, and it was such a struggle, I haven't tried it since.