Toss together the mozzarella, feta, lemon zest, and basil in a medium-size bowl.
For each sandwich: Brush olive oil on two slices of bread to flavor the outside of the sandwich. Flip over one slice and top the other side with a layer of the cheese mixture. Close the sandwich with the other slice of bread, oiled side up.
Grill two panini at a time, with the lid closed, until the cheese is melted and the bread is toasted, 4 to 5 minutes.