This would work for lemons too. I'm not too sure about the keeping qualitites but it only makes about 1 litre and it doesn't last long in our house anyway.
1.5 cups lime juice
1.5 cups water
3 cups sugar
Combine the ingredients in a saucepan over a medium heat.
Stir until sugar is dissolved.
Bring to the boil then remove from heat.
Pour into warm sterilised bottles.
To serve dilute with chilled water or chilled soda/mineral water. This would make a delicious summer drink but we never have any left by the time summer rolls around.