Combine the sugar in a medium saucepan, then zest the lemons directly over it. Using your fingertips, rub the zest thoroughly into the sugar to draw out the fragrant oils. Pour the freshly squeezed lemon juice into the pot and blend gently until the sugar is moistened. In a separate bowl, crack the eggs and add the salt, beating vigorously with a fork to break down as much of the egg white as possible. Incorporate the beaten eggs into the sugar mixture and whisk until smooth. Place the pot over low heat and cook, stirring continuously, until the curd thickens and reaches 170°F on an instant-read thermometer or coats the back of a spatula. Cut the butter into slices and set them in a clean bowl, then position a fine mesh sieve over the bowl. Strain the hot curd through the sieve onto the butter, discarding any zest or cooked egg bits. Stir patiently until all the butter has melted completely into the curd. Transfer the finished lemon curd into an airtight container and refrigerate. It will keep well for up to two weeks, or longer if frozen.