Use of biological machines and environments in novel bioinorganic nanostructures is critical for development of new types of biosensors, bio-NEMS devices, and functional materials. Lipid bilayers that mimic a cell membrane have already played an important role in such applications. We present supported lipid bilayers that spontaneously assemble in a continuous nanoshell around a template of a carbon nanotube wrapped with hydrophilic polymer cushion layers. We demonstrate that such 1-D lipid membranes are fluid and can heal defects, even over repeated damage-recovery cycles. A simple diffusion model can describe mobility of lipid molecules in these 1-D nanoshells. These structures could lead to the development of new classes of biosensors and bioelectronic devices.