Combine vegenaise or mayonnaise with wasabi paste in a small bowl. Set aside. Cut each strip of eel into 4 pieces of 2 inch lengths. Drizzle lemon juice and sprinkle dill weed over eel.
Fill a large bowl with water. Add 2 tablespoons of vinegar to the water. Use this to wet hands to prevent rice from sticking to them. Take a small handful of rice in one hand and gently mold into a rounded oblong. Place it down on a plate.
Lay a piece of eel across fingers and dab a little wasabi mayo on the bottom side. Gently press ball of rice onto eel.
Turn the sushi around so that the topping is on the top. Squeeze the sides of the sushi between index finger and thumb to shape and compact rice. Cup the sushi in left hand and use two fingers to press gently on the topping to further compact it.
Repeat to shape sushi. Decorate with capers if desired.