Trim and peel pineapple. Cut lengthwise into quarters and remove the tough core. Cut each quarter in half crosswise, making 8 sections.
Combine lemon zest and sugar in a ziplock bag. Rub vigorously to blend flavors.
Prepare a charcoal fire, let burn to a gray ash and set grill about 6 inches from heat source. (Alternatively, set a stove-top grill pan over medium-low heat.)
Working with one or two sections at a time, place pineapple in bag with sugar mixture and turn carefully to coat. Transfer to grill and cook, flipping often, until caramelized and slightly softened, 5 to 7 minutes. Cool slightly before serving.