In a medium pot, combine 3 cups (720ml) water with the ginger, chamomile, marshmallow root, cinnamon, apple cores, thyme, sage, and lemongrass. Bring to a boil. Reduce to a vigorous simmer, and cook until reduced to ¾ cup.
Pour the hot herbal water through a fine mesh sieve, and discard the strained out bits, preferably into compost if you keep one.
Stir in the honey and lemon juice to the warm herbal water. If you let it cool to long, you can warm it with the honey and lemon juice in a small pot just enough to help the honey mix in. Do not let it come to a boil or the syrup will taste bitter.
Transfer the syrup to bottles, and store in the fridge for up to 2 months. Shake well before using.