Line a baking sheet with wax paper and place a wire rack on top.
Combine sugar, lemon zest, cinnamon stick and water in a small saucepan; bring to a boil, stirring to dissolve the sugar. Reduce the heat to medium and simmer for 3 minutes. Add apricots and gently simmer just until tender, 6 to 8 minutes. Transfer the apricots with a slotted spoon to the rack. Let cool completely.
Melt chocolate in a small metal bowl set over a pan of barely simmering water. Dip half of a poached apricot in the chocolate, letting excess drip off. Sprinkle some chopped pistachios over the chocolate half and return the apricot to the rack. Repeat with the remaining apricots. (You will have some melted chocolate left over.) Refrigerate until the chocolate has set, about 20 minutes.
Make Ahead Tip: The candies may be stored in an airtight container, with wax paper between each layer, in the refrigerator for up to 1 week.