Short answer - YES. It can be invasive by its roots PLUS its seeds.

Lemon balm does spread by seed and by root as Daisy mentioned. How vigorously it or any other plant spreads is location & condition dependent.

Lemon balm does spread for me, but it isn't anything that I can't keep in check or harvest away. In your location it may be more vigorous or less vigorous - I can't say. If you are concerned about an unwanted spread, then keep it contained.

FataMorgana

If you control reseeding by lopping off the flowering stems after the bees are done with them, lemon balm is not difficult to handle. The mounds get bigger every year, so you do have to thin it back. I find it much less invasive than any mint.

I have a large patch of lemon balm (over 1000 square feet) planted in fall 2007, and I've seen no evidence of it spreading by root, here in Maryland. It certainly does self-seed all over the place, but in that regard it's just one among many weeds that pop up.

Incidentally, the lemon balm was originally interplanted with catnip. It was thriving last year, but absolutely none of the catnip came back this year. I'm assuming it drowned because of the unusual snow cover last winter. The lemon balm is so vigorous that I was regretting planting it with the catnip. But if I had planted only catnip, I wouldn't have anything there now.

While many sources say catnip is a perennial, I find it to be more of a biennial or a short-lived perennial. It could have just run its course and the seedlings from its dropped seeds could not compete with the more vigorous lemon balm.

FataMorgana