Add the sugar and ¾ cup water to a medium-sized pot and bring to a boil over medium-high heat. Reduce to a simmer and stir occasionally, cooking until the sugar has completely dissolved (this should only take about 5 minutes). Remove from heat and let simple syrup cool.
To a large pitcher, add 1 cup lemon juice, 1 cup of the simple syrup, and 3 cups of cold water. Stir well, then taste. If this is the level of sweetness you’d prefer, stop here. If it’s a little too sweet for your tastes, add 1 ½ - 2 cups more of water. I find for me, 5 cups of water is the perfect balance of sweet and tart. You may have a little bit of simple syrup leftover (save and refrigerate for a cocktail if you like). Add some of the the lemon slices and stir. Serve over ice, adding a lemon slice or two to each glass. Store lemonade in the refrigerator (it should keep for several days).
*If using Meyer lemons, gradually add the simple syrup to taste (starting with the full amount will likely make the lemonade too sweet, as Meyer lemons are sweeter than regular lemons).