Spherical bodies such as bubble, solid sphere and droplet moving in shear flow are experiencing a force normal to their relative motion, called lift force. When varying the viscosity ratio between the droplet and the external fluid, we report for droplet Reynolds number of order 100 an unexpected lift force peak at a viscosity ratio of order unity. We reveal thanks to a detailed inspection of the flow field obtained using direct numerical simulation that this behavior is related to an internal 3D flow bifurcation also observed under uniform-flow conditions. In the presence of an ambient shear, this internal 3D bifurcation results in the amplification of the vortex tilting-stretching mechanism responsible for the lift force, making the trailing vortices generated in the droplet wake stronger, and as a consequence an enhanced lift effect.