In a large bowl, mash the cream cheese with sugar until thoroughly combined; stir in the lemon juice, and mix in the yogurt, about a cup at a time, until the mixture is smooth and creamy. Mix in the cherries. Cover the bowl with plastic wrap, and chill until very cold, at least 4 hours.
Pour the mixture into an ice cream freezer, and freeze according to manufacturer's instructions. For firmer texture, pack the frozen yogurt into a covered container, and freeze for several hours.