Lemon balm is a perennial native of Southern Europe that has been used for centuries as a medicinal herb. It is used in teas and garnishes and its oil is used in perfumes and in antibacterial and antiviral preparations. Gardeners often kill this fragrant member of the mint family, however, because it can also become invasive and crowd out other herbs and plants in the garden. Should you need to eradicate a stand, patience and persistence are often your best tools.
Stop the spread of runners---roots that grow just under the surface and put up new plants from nodules that rise to the surface. Pull new plants as they grow, excavating and removing the entire root system of each plant before it has time to establish colonies. Cultivate the area frequently, pulling out roots and plants throughout a growing season.
Keep lemon balm and the area around it completely dry and as warm as possible. Lemon balm's cultural needs---the conditions and care it needs to grow---are few but it does like moist, cool soil and partial shade.
Shear off lemon balm's white or yellow flowers as they appear. Once plants flower, they'll begin setting tiny, numerous seeds. Destroy both the cuttings and the seeds to avoid spontaneous rooting and volunteer germination.
Pull plants, then cover the lemon balm patch with newspaper to cut off light that plants need to grow and seeds need to germinate. After a week or two, everything under the paper should be dead---and any roots that have extended beyond the edges should have sprouted.
Use broadleaf weed killer as a last resort because it can harm other garden plants or stay in garden soil. Look for an herbicide that is safe for use around vegetable crops.