In small saucepan, combine apricots and water. Cook over med heat 15-20 mins or until tender, stirring frequently. Drain and puree apricots. Set aside.
While apricots are cooking, grease and flour a 9-in square pan. In a small bowl, combine flour, baking powder, baking soda and salt. In large bowl, beat sugar and 1/3 cup butter until light and fluffy. Add vanilla, lemon extract and egg, beat well. Alternately add dry ingredients and 2/3 cup water to sugar mixture. Stir in 3 Tablespoons of apricot puree. Pour batter into prepared pan.
Bake for 25-35 minutes or until done. Cool slightly.
FROSTING: In small saucepan, combine brown sugar, 2 Tbls butter and remaining apricot puree. Bring to a boil and boil for 1 min, stirring constantly. Remove from heat and stir in coconut. Immediately spread over warm cake.