Blend the apricots, sugar, sherry vinegar, Dijon mustard, salt and lemon juice in a food processor. With the motor running, drizzle in the olive oil until it emulsifies into a creamy consistency. If preparing in advance, refrigerate in a sealed container, and whisk well before serving.
In a large bowl, stir together the wild rice, apricots, almonds, dried cranberries and goat cheese. Dress with several tablespoons of Apricot Dressing. Season to taste with fresh pepper and salt, if desired.