In a small saucepan, combine 1 cup water and honey. Heat over medium heat, stirring occasionally, until the honey completely dissolves into the water, about 3-4 minutes.
Remove the saucepan from heat and stir in the dried lavender buds. Cover and let steep for exactly 5 minutes to infuse the floral flavor without bitterness.
Strain the lavender honey syrup through a fine-mesh sieve into a heat-safe bowl or measuring cup, pressing gently on the buds to extract all the liquid. Discard the lavender buds and let the syrup cool for 10 minutes.
While the syrup cools, juice the lemons through a strainer to catch seeds and large pulp pieces. You should have about 1 cup of fresh lemon juice.
In a large pitcher, combine the cooled lavender honey syrup, fresh lemon juice, and 4 cups cold water. Stir vigorously until everything is well blended and the syrup is fully incorporated.
Taste and adjust sweetness or tartness if needed by adding a tablespoon more honey or lemon juice. Refrigerate for at least 30 minutes before serving to allow flavors to meld.
Serve over ice, garnished with lemon slices and a small lavender sprig if desired. Stir gently before pouring as the honey may settle slightly.