Most of the small craft that I see in the pictures are painted on the outside. Is there something about the Lapstitch construction that requires this?

Nothing about the LapStitch process prohibits you from varnishing the exterior. Lo, these many photos we have here of such boats. If you can varnish the interior, you may certainly varnish the exterior.  Ultimately it's up to your preference because all CLC kits are shipped with varnish-grade materials.

The reason so many of the boats are painted is that the all-varnish look is a bit overwhelming, like too much makeup on a pretty girl. The wood texture is a very strong statement, and the nice hull shape is lost in all the noise.

When you paint the exterior, your eye is drawn to the long, graceful sweeps of the planks. If you paint with a light color, the laps of the planks cast lovely shadows. It's a traditional, nuanced, sculptural treatment, and with acres of varnish on the interior no one will doubt that you've built a wooden boat.