Lemon grass is not generally invasive. However, in some climates and conditions it is disasterously invasive. In the Caribbean island of Antigua, lemon grass, Cymbopogon citratus, was introduced in the last century. It has now devastated aroud 2,000 acres of countryside. Climate is something to do with it, but the biggest problem is that it is highly flamable because of the oils in it and when fires occur, it is about the only species able to recover - hence you see previously beautifully biodiverse forested hillsides covered in this grass and nothing else - completely useless for agriculture or as wilderness area. So this may not be a problem for most people, but in dry areas, do take care.