In classical French cooking, Meunière Butter (“beurre meunière”) is a very simple sauce of browned butter (aka “Beurre Noisette”) flavoured with lemon.
You make it by melting butter until it has started to brown, and seasoning it to taste with salt, white pepper and a few drops of lemon juice.
It’s used in fish “à la meunière” dishes, and for some vegetables that have been either poached or cooked in butter.
You want white pepper rather than black as the white has a more winey taste that compliments the butter, and the black would look like fly specks in this.
The butter will appear to brown more after you add the lemon juice to it. The butter will develop brown bits in it; don’t strain those out. Those are the flavour bits you are working to develop.
In this regard, it’s the opposite of Indian “ghee butter”, where you strain the solids out deliberately so that there are none to brown.
“Meunière” means “miller’s wife.”