text: I'm not familiar with whether it out-competes native ground covers or dies out over time if not maintained, but if it spreads outside the lawn and takes over the surrounding area, that would be invasive.  It is a matter of degree, of course.  A clear example of invasiveness is the purple vetch that spreads in large patches, completely covering the ground, without any help from humans.  I'm not sure if merely surviving qualifies a non-native plant as invasive, or if it has to actively displace and/or harm native flora and fauna.