Someone who's lusty is healthy and passionate. A lusty young farm worker is strong and energetic, tackling each new challenge enthusiastically.
You can be lusty in love, yearning for or infatuated with another person. You can also be lusty for life, filled with great strength and eager to live each day to the fullest. As time has gone by, lust and lusty have gained the "full of desire" meaning and lost some of the thirteenth century "joyful" sense of the words.