My favourite method for making a smooth 3rd person camera is fairly simple and straightforward – camera position is calculated relative to the character position. Here is a short demo, the camera motion is in lines 109-112:
cameraAngle = THREE.MathUtils.lerp( cameraAngle, angle, 0.01 );
camera.position.setFromSphericalCoords( 15, 1, cameraAngle );
camera.position.add( character.position );
camera.lookAt( character.position );
https://codepen.io/boytchev/full/RwErNZM
