How to determine the right spec of a servo motor given an inertia moment?
Inertia doesn't matter very much given the way this is set up. (Side note, it's \$kg\ cm\$  not \$kg/cm\$, and it's really kg on earth, so it works out as a unit of torque, albeit a silly one). You know the mass of the lid, work out the length of the lever arm being applied to the lid to lift it. Convert the mass to kg, lever arm length to cm, multiply them together, give yourself some safety factor (~20%), buy a servo with that \$kg \ cm\$ rating or higher.