Heat apple cider, lemon juice and onions in a fondue pot until bubbly. Add cheese by handfuls, stirring until melted. Repeat until all cheese is melted. Mix cornstarch and mustard in 1/4 cup apple cider. Add to cheese mixture; stir until mixture thickens. Add white pepper, to taste and adjust seasonings. Reduce heat to low to keep warm. Serve with sliced apples, fruit, or an assortment of breads.