Which of the following helped lower-class Athenians gain democratic rights in the government of the city-state?

While it is true that having armor and equipment could elevate a citizen's status in the military, this option primarily pertains to the wealthier citizens who could afford the expenses associated with becoming a hoplite. Lower-class Athenians typically could not afford this and thus did not gain democratic rights through this means.

Threatening to immigrate to Sparta was unlikely to yield any significant change in Athenian politics. Instead, such a threat would be more of a bluff than a viable strategy, as it would not address the immediate need for lower-class Athenians to assert their rights within their own city-state.

Although upheaval against the upper classes did occur in various forms, it was not the primary means by which lower-class Athenians gained democratic rights. The Athenian democracy evolved more through reforms and the recognition of the contributions of lower classes, rather than outright overthrowing the elite.

While working on the Acropolis was significant for cultural and religious reasons, this labor alone did not directly translate into political rights. The construction projects mainly served to enhance the city-state's prestige rather than empower the workers politically.