Smoked Fish Fritters with Beet Vinaigrette

Name: Smoked Fish Fritters with Beet Vinaigrette
Ingredients: 2 medium red beets (about 8 ounces total); 1/4 cup fresh lemon juice; 2 tablespoons prepared horseradish; 1 tablespoon Sherry vinegar; 1/2 cup extra-virgin olive oil; Kosher salt; 1 12-ounce skinless cod or pike fillet; 5 tablespoons (or more) vegetable oil, divided; 8 ounces smoked whitefish, skin and bones removed, flaked; 3 large eggs, beaten to blend; 1 large shallot, finely chopped; 1 piece matzo, finely crushed (about 1/4 cup); 1/4 cup chopped fresh chives; 2 tablespoons chopped fresh dill plus more for serving; Freshly ground black pepper