I think support in symbolism is often times displayed as strength. Lelouch's grip is a little too molesty to properly emit the idea, 'Support.' I think vulnerability is a good guess, otherwise he could just be molesting the sword.

It could be something in how his strength is a soft one: commands, manipulation, obfuscation. But Suzaku's is more hard: physical strength, martial arts, endurance.

Could be anything.