Position an oven rack in the middle position, and preheat oven to 350°F. Generously butter the bottom and sides of a 10-inch pie plate.
Rehydrate the diced apricots in a small bowl with warm water to cover. Let sit for 5 minutes, then drain the water and spread out apricots on a clean towel to dry the pieces on all sides. You want to get them as dry as possible. (This is optional if your dried fruit is soft and pliable.)
Combine the flour, baking soda, and salt in a small bowl. Whisk gently to thoroughly incorporate the ingredients.
Combine the melted butter, sour cream, and 7/8 cup of sugar in a large bowl and mix will to combine. This can be done either by hand with a sturdy whisk or a hand mixer.
Add the eggs, one at a time, mixing well after each addition. Add the almond extract and lemon zest.
Add the flour mixture and mix gently until well incorporated but taking care to avoid over-mixing. Fold in the dried apricots.
Pour the batter into the prepared pie plate and smooth to level the surface. Sprinkle the sliced almonds atop in an even layer; then sprinkle on the remaining 1/8 cup of granulated sugar in a thin, even layer on top of the sliced almonds.
Bake for about 30 minutes until a toothpick inserted into the center of the cake comes out clean, and the cake and almonds are golden brown.
Cool completely before slicing.