We report a new class of dynamically reconfigurable complex colloids comprising immiscible liquid crystals (LCs) and fluorocarbon oils. Producing stable spherical droplets requires the utilization of appropriately designed surfactants to reduce the high intrinsic surface tension between the LCs and the fluorocarbon oils that initially lead to nonspherical, "snowman-shaped" Janus droplets. After stabilizing the interfaces via surfactants, the LC droplet morphology can be dynamically switched between LC-in-fluorocarbon-in-water double emulsions (LC/F/W), spherical Janus emulsions, and inverted double emulsions (fluorocarbon-in-LC-in-water, F/LC/W) in response to changes in the surrounding surfactants. These stabilization methods can be extended to smectic LCs to create droplets with more complex internal arrangements and expand the range of LC emulsions that can be prepared. In addition, by using new mesogenic surfactants that control the LC director field at each LC interface, we prepare LC complex colloids exhibiting different internal configurations. The ability to control the LC anchoring conditions made it possible to create topological singularities as powerful templates for the precision assembly of antibodies at the droplets' interface. These dynamic LC complex colloids of controllable morphology and LC orientation are rich soft material platforms that will find utility in a variety of sensing applications.