Using a sharp paring knife, trim off top and bottom of lemons. Stand fruit on end and carefully cut the peel and white pith from flesh, following curve of fruit from top to bottom. Trim away any remaining pith. Cut each section away from membranes, cutting as close to membranes as you can, then cut fruit pieces in half crosswise and place in a large bowl. 

To the bowl, add chicken, bell peppers and cheese. Add oil, marjoram leaves and 1 teaspoon salt; toss to combine.  Season to taste with black pepper and more salt if desired.