When you scale the recipe (since I don't think you want to make 3 cups), add a little more fresh lemon juice to get a more of that flavor. Add fresh thyme right before you add the butter, and I would recommend blending in the butter vs. whisking in the butter so that you get more flavor from the thyme.
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If you google beurre blanc, you'll get the basic sauce recipe. At that point, you can add almost any herb or spice you care for. I'd use lemon zest rather than lemon juice at first...and then taste for flavour. You can always add more, but can never take away. As for the thyme, add it right at the end, using only fresh, please...never dried!
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ok, since you are going to go ahead with the recipe... i would approach as ironchef but i would also encourage the use of grated lemon zest to get the lemony flavor, be sure to only grate the yellow part