Steam clams with 1 cup water in a covered kettle over high heat, shaking the kettle occassionally, for 7-8 minutes, or until shells open. Discard any unopened shells. Let clams cool, then remove the meat and discard the shells. Mince the meat.
In a skillet, cook bacon over moderate heat, stirring occasionally, until crisp and golden brown. With slotted spoon, transfer bacon to paper towels to drain. Reserve bacon fat in a small heat-proof bowl.
In the skillet, heat 1 tablespoon of the reserved fat over moderately low heat and cook onions until soft. Transfer onions to a large bowl.
Drain potatoes well and pat dry. In the skillet, heat 2 tablespoons of the reserved fat over moderately high heat. Cook potatoes, stirring, until tender, then transfer to bowl with onions. Stir in bacon, clams, 1 tablespoon of the parsley, eggs, add salt and pepper to taste.
Blend thoroughly. Heat a large griddle or heavy skillet over moderately high heat. brush hot griddle with some of the reserved fat. Drop several 1/4 cups of clam mixture onto griddle and with a fork, pat into neat 1/4 inch thick cakes. Cook cakes, 1 minute on each side, or until golden brown.
Repeat with remaining clam mixture. (The cakes may be made several hours in advance, kept loosely covered on a baking sheet and re-heated in a preheated 300 ° F oven).
In a small saucepan, melt butter over moderately low heat. Stir in horseradish, the remaining 1 tablespoon parsley and lemon juice. Drizzle over clam hash cakes. Garnish cakes with lemon slices and parsley sprigs if desired. Serve 8.