Yes, you'll have to use multiple lights to achieve this, faking the reflected light. Computing real reflected light isn't built in (and computationally very complex/expensive). You have a variety of options.
A second directional light that could always be in the opposite position and direction of your sun.
A hemisphere light that remains constant. Hemisphere lighting gets a sky color and a ground color and intensity and adds a nice extra bit of depth to your lighting.
// sky color ground color intensity
hemiLight = new THREE.HemisphereLight( 0x0000ff, 0x00ff00, 0.6 );
here's a working example https://threejs.org/examples/#webgl_lights_hemisphere
you could use any combination of different lights but be careful there's a performance trade off.
It's also worth mentioning half-lambert shading which is enabled by setting the wrapAround property to true in your material. This gives a nicer falloff to black that results in less harsh lighting. More mid tones and less blacks.