Final answer:
Special sessions of the legislature are typically called by the governor, although the rules can vary by state. The lieutenant governor usually cannot convene special sessions, and the legislature itself may or may not have the power to initiate them, depending on state laws.
Step-by-step explanation:
Special sessions of the legislature can vary by state in how they are convened. In some states, only the governor has the power to call a special session, whereas in other states, the power is shared between the legislative and executive branches. However, it is generally not within the authority of the lieutenant governor to convene special sessions unless they are serving as acting governor due to the incapacitation of the governor.
Regarding the option that special sessions can only be called when the legislature fails to develop a working budget during a regular session, this is not typically the sole reason for their convening. Special sessions may be called for various reasons, such as addressing budgetary issues during an economic downturn, creating redistricting plans, or dealing with urgent issues that need immediate attention.
The ability of the legislature to initiate special sessions varies by state. Some states may allow the legislative branch to call for a special session upon a supermajority vote, but this is not a universal rule across all states.
Therefore, the most accurate answer to which option is correct is that special sessions can only be called by the governor, keeping in mind this is subject to state-specific variations.