Put the balsamic vinegar and honey in a small bowl. Whisk in the olive oil. Season with salt and black pepper. Set aside. Combine the sun-dried tomatoes, tuna and chickpeas in a medium bowl and mix to combine. Add the vinaigrette and gently toss. Set aside.
Remove the peel and pith from the Meyer lemons and thinly slice.
Lay the arugula on a large platter. Arrange the tuna mixture over the top while tucking the lemon slices in between. Sprinkle the parsley over the top and sides and season with freshly ground black pepper.