I could have sworn I responded to this post this morning. Anyway, check the site below about 1/2 way down the page. They give the supplier to Starbuck's & then post a recipe but I don't know how close it is to the one you want since they say the supplier never gives out recipes (naturally.)

Here is a link that might be useful: Pound cake

This isn't Starbucks, but I've made it a couple of times, and it's received rave reviews.

Here is a link that might be useful: Cooks Illustrated Lemon pound cake

I really love most cooks illustrated recipes I have tried....but you have to be a paying member to view that page.
Linda C

Is anyone a paying member who has this lemon pound cake recipe?

I think this is it.

Lemon Pound Cake
Published: March 1, 2002
Makes one 9 by 5-inch cake, serving 8

You can use a blender instead of a food processor to mix the batter. To add the butter, remove the center cap of the lid so it can be drizzled into the whirling blender with minimal splattering. This batter looks almost like a thick pancake batter and is very fluid.
INGREDIENTS
16 tablespoons unsalted butter (2 sticks), plus 1 tablespoon, softened, for greasing pan
1 1/2 cups cake flour (6 ounces), plus 1 tablespoon for dusting pan
1 teaspoon baking powder
1/2 teaspoon table salt
1 1/4 cups granulated sugar (8 3/4 ounces)
2 tablespoons grated lemon zest plus 2 teaspoons juice from 2 medium lemons
4 large eggs
1 1/2 teaspoons vanilla extract

Lemon Glaze (Optional)
1/2 cup granulated sugar (3 1/2 ounces)
1/4 cup lemon juice , from 1 or 2 medium lemons

See Illustrations Below: Glazing Pound Cake

1. Adjust oven rack to middle position and heat oven to 350 degrees. Grease 9 by 5-inch loaf pan with 1 tablespoon softened butter; dust with 1 tablespoon cake flour, tapping out excess. In medium bowl, whisk together flour, baking powder, and salt; set aside.
2. In glass measuring cup or microwave-safe bowl, microwave butter, covered with plastic wrap, at full power until melted, 1 to 2 minutes. (Alternatively, melt butter in small saucepan over medium heat.) Whisk melted butter thoroughly to reincorporate any separated milk solids.
3. In food processor, process sugar and zest until combined, about five 1-second pulses. Add lemon juice, eggs, and vanilla; process until combined, about 5 seconds. With machine running, add melted butter through feed tube in steady stream (this should take about 20 seconds). Transfer mixture to large bowl. Sift flour mixture over eggs in three steps, whisking gently after each addition until just combined.
4. Pour batter into prepared pan and bake 15 minutes. Reduce oven temperature to 325 degrees and continue to bake until deep golden brown and skewer inserted in center comes out clean, about 35 minutes, rotating pan halfway through baking time. Cool in pan for 10 minutes, then turn onto wire rack.
5. If using lemon glaze, while cake is cooling in pan, bring sugar and lemon juice to boil in small nonreactive saucepan, stirring occasionally to dissolve sugar. Reduce heat to low and simmer until thickened slightly, about 2 minutes.
6. After turning cake onto wire rack, poke the cake's top and sides with a toothpick and brush on Lemon Glaze (see illustrations below). Cool to room temperature, at least 1 hour. (Cooled cake can be wrapped tightly in plastic wrap and stored at room temperature for up to 5 days.)

Thank you!

I can't believe I found this post. I think their lemon pound cake is wonderful! So dense and good. I like it without the icing.

Thanks for the recipe!
Carla