Peel the lemons with a lemon zester and set peels aside. Then peel off the remaining white pith, just like you would peel an orange. Throw out the pith and then slice the lemon pieces and lemon peel into thick chunks.
Mix the lemon chunks, lemon peel, salt, and sugar in a small glass or plastic bowl and mix until everything is combined. Cover the mixture and refrigerate for at least 20 minutes but up to 2-3 weeks.