Lively, animated, vivacious, sprightly, gay denote in common keenly alive.
Lively suggests especially briskness, alertness, or energy.
Animated applies especially to what is also spirited or bright.
Vivacious and sprightly suggest greater lightness of spirits or quickness of wit; they apply especially to manner or language.
Gay implies utter carefreeness and exuberant or overflowing spirits.