Begin by rinsing the thyme. You can either add to a colander and rinse with cold water, or add to a bowl of cold water and swirl to remove any debris.
Add the fresh thyme (leaves and stems) to a small saucepan with two cups of filtered water. Bring to a boil, then reduce the heat and simmer until liquid is reduced in half to about 1 cup. This should take about 20-30 minutes.
Remove from heat and allow to cool.
While the thyme tea is simmering, add the sliced lemons to a clean glass jar. Pour the honey over the lemons and allow to sit. The honey will macerate the lemons and draw out the oils from the peel.
Once the thyme tea is cool, strain the thyme leaves and stems from the tea. Add the tea to the jar and stir to combine. At this point, you can either remove the sliced lemons, or you can allow them to sit on the syrup for up to 24 hours, then remove. The longer they sit, the stronger the lemon flavor will be.
Your cough syrup is ready! You can add a fresh thyme sprig to the jar if desired.Yields approx. 1½ cups.