The correct answer is C) motor starting circuits. Time lag fuses, also known as dual-element fuses, are necessary in motor starting circuits due to the high in-rush current that occurs when a motor is first started. This high initial current can cause standard fuses to blow prematurely, even though the steady-state operating current may be well within the fuse's rating. The time lag feature of these fuses allows them to withstand the brief high-current surge during motor startup, preventing nuisance tripping and ensuring the circuit is protected under normal operating conditions. The other options are incorrect because emergency lighting, main lighting, and general alarm circuits do not typically experience the same high in-rush currents that require time lag fuses for protection.