Combine the mayonnaise, horseradish, 2 teaspoons of the lemon juice and plenty of black pepper.
Toss the apple thoroughly in the remaining lemon juice to prevent browning.
Cut the roast beef into strips about 1-inch wide and 5-to 7-inches long.
Place an apple slice and a few arugula leaves on the short end of each strip -- they should stick out on the edges -- and spoon about 1/2 teaspoon horseradish cream over.
Roll up and spear with a toothpick.
Wrap tightly and refrigerate until ready to serve.