In a medium saucepan, combine the water and sugar and bring to a simmer, swirling the pan once or twice. When the sugar has dissolved, add the lemon juice and zest. Decrease the heat until the syrup is barely simmering; add the peaches and cook, uncovered, for about 15 minutes, until the peaches are tender. Remove the pan from the heat and let the peaches cool in the liquid for 30 minutes. Remove the cooled peaches with a slotted spoon, and chop into small pieces and place in a bowl. With a wooden spoon, carefully fold the banana and yogurt into the peaches until blended.

Serve immediately. Freeze leftovers that won't be eaten the next day.