Sterilize 4 pint-sized jars and their lids according to the manufacturer's instructions.
Evenly trim the ends of the green beans to fit the jars. Divide and pack the green beans, rosemary, garlic, and lemon peels among the jars.
Bring a large pot or canner of water to a boil.
In a medium pot, combine the water, vinegar, salt, and sugar and bring to a boil. Simmer for 2 minutes, stirring to dissolve the sugar and salt. Ladle the hot mixture into the jars, leaving a 1/2-inch headspace. Wipe the rims with a clean cloth, affix the lids and seals, and seal tightly. Process the jars in the hot water bath for 15 minutes. Carefully remove with tongs and set aside to cool. Let sit in a cool, dark place for at least 3 weeks before opening.
Yield: 4 pints