Toss together the arugula with the feta and the onion.
Light the grill to medium-high. (Alternatively, you can grill the watermelon in a grill pan on top of the stove.) Cut the watermelon in large triangular wedges about an inch thick.
Using paper towels, blot the watermelon wedges dry
Brush the watermelon slices with a little olive oil on both sides.
Grill the watermelon slices over high heat for a few minutes, turning each wedge with kitchen tongs, until grill marks appear. Cut the wedges into smaller triangular serving pieces.
Make a dressing by whisking together the rest of the olive oil with the lime juice and zest. Season with salt and pepper.
Toss the arugula mixture with all but 2 tablespoons of the dressing and transfer to a serving platter or large bowl.
Place the grilled watermelon over the arugula mixture. Drizzle with remaining dressing and serve.