I haven't done lemon balm but have rooted rosemary and basil in water. It takes a bit of time I think though. Change the water regularly and give it another couple of weeks and hopefully you'll see them starting to grow.
I agree, it will grow anywhere and everywhere. Just pull up a bit from the roots, stick it in another hole in the garden and I am sure it will take. Don't bother buying the root stuff! Smells nice though.
It's better for roots to be kept in dark - sorry I didn't make it clear, and although most plants like light, they don't need it to root. Generally, roots are stronger if grown in soil, although it can be quicker in water, they have minor shock when planted into soil to grow.