Stir together mayonnaise, mustard and lemon juice in small bow. Set aside.
Sprinkle salt in bottom of microwave egg cooker or microwave-safe bowl or mug. (Salt attracts microwave energy and helps to cook egg withe without cooking yolk completely). Break egg into egg cooker. Pierce yolk and white to bottom of cooker several times with fork. (Piercing is necessary to prevent egg from "exploding" during cooking.) Place lid on cooker base, lining up notches. Twist to secure (or cover with microwave-safe plastic wrap if using a bowl or mug).
For a soft boiled egg, microwave on High (100% power) for 35 seconds or on Medium (50% power) for 1 minute. Egg yolk should still look soft, while egg white should be almost cooked; white will finish cooking as egg stands. If egg is still quite undercooked, turn egg over and microwave for 10 seconds more at same power level.
To hard boil egg, cook for additional increments of 10 seconds until egg yolk and white are nearly fully cooked.
Spoon sauce over cooked egg in cooker. Cover and leave egg and sauce in cooker for 30 seconds before removing and placing on toasted English muffin half topped with ham.