Which tempo marking indicates a lively character?

The tempo marking "Animato" indeed indicates a lively character. The term derives from the Italian word "animare," which means "to enliven" or "to give life." When a piece is played with this marking, it often carries a sense of buoyancy and spirited movement, creating an upbeat and energetic feel.

In contrast, the other options represent different expressive qualities that do not specifically convey the same liveliness. For instance, "Allegretto" suggests a moderately fast tempo but is typically more relaxed than "Animato." Similarly, "Appassionato" communicates a passionate and intense expression, which can imply a slower, more dramatic interpretation rather than a lively one. "Assai" means "very," and is often used in conjunction with other terms to modify their intensity, but on its own, it does not define a specific lively character. Thus, "Animato" is the most appropriate choice to convey a lively and energetic tempo.