African lilies can spread, yes. But they do not do so quickly or aggressively, so you do not need to worry about them taking over your garden. The University of Florida says, “Left undisturbed, this lily will multiply to form large clumps. These look wonderful when planted in groups in landscape beds but work equally well in containers. Individual plants seldom spread wider than 2 feet, but clumps can fill entire beds over time.” Despite the fact that this is not a particularly aggressive plant, there are still some areas where it is classified as invasive. There is some controversy in New Zealand regarding whether or not it should be considered a “pest plant.”