Slice butter into 6 pieces. Use your smallest skillet or pot, and place it on medium-low heat. Add 1 piece of butter, and after it melts add the garlic and onion. Gently sauté until translucent. It should not get too brown.
Add white wine vinegar, lemon juice, and water, and reduce to less then a quarter cup of liquid.
Reduce the heat even further. Add 3 more pieces of butter and whisk until smooth. Add the remaining 2 pieces and whisk. Remove from heat. Add salt and pepper to taste.
Serve immediately, or store sauce up to 2 hours at room temperature. Reheat gently. Do not bring to a boil or the butter will split from the emulsion.
Note that my recipe is alcohol free. It calls for white wine vinegar rather than white wine, which is the typical. This is why I add water to dilute the intensity of the vinegar. I do recommend that you use a wine-style of vinegar for its robust flavor. If you wish to use regular white wine, simply replace the water and vinegar part with wine.
Add a tiny bit of boiling hot water to reheat the lemon butter sauce just before serving.