What musical term indicates a lively tempo faster than allegro?

The musical term that indicates a lively tempo faster than allegro is vivace. Vivace is typically understood to denote a brisk, animated pace, and it often implies enthusiasm and energy in the music. Generally, when tempos are categorized, allegro represents a lively tempo, usually around 120 to 168 beats per minute. Vivace, which translates to "lively" in Italian, is used to convey an even faster tempo, often exceeding 168 beats per minute, making it appropriate to label it as faster than allegro.

As for the other terms in the choices, andante indicates a moderately slow tempo, typically slower than allegro, while allegretto is a tempo that is moderately fast but not as fast as allegro. Presto signifies a very fast tempo, even faster than vivace, but since vivace fits the criteria of being lively and specifically faster than allegro, it is the correct answer in this context.