Ask Mr. Smarty Plants

Any plant being grown in ideal conditions for it without controls can become invasive.The Lady Bird Johnson Wildflower Center expertise is limited to care and propagation of plants native not only to North America but also to the area in which the plant is being grown. 

Before we go any further, let's establish what in your garden is native where, and then try to help you control the invasive ones.

Rudbeckia hirta var. pulcherrima (blackeyed Susan) is native to Virginia, although we could not find county areas for it in the USDA Plant Profiles on the plant. It needs full sun to part shade, and sandy or loamy soil. It is a biennial, meaning it has a rosette close to the ground the first year and blooms the second year. If it is happy where it is growing, it will perennialize.

Salvia guaranitica, known variously by trade names such as Black and Blue sage and Blue Anise Sage. It is native to Brazil, Paraguay and northern Argentina, and is, indeed, considered very invasive. 

The Oriental members of the genus lilium are auratum, native to Japan, speciosum, native to Japan and China, and lancifolium (Tiger Lily) native to Japan, China and Korea. Since we would have no information on them in our Native Plant Database, we found two websites that might help you in identifying why your lilies disappeared: University of Minnesota Extension, Selecting Lilies for Your Garden, with cultural requirements for lilies; and Botany.com Genus lilium.

So, in your garden you have one plant native to Virginia, Rudbeckia hirta var. pulcherrima (blackeyed Susan), which belongs where it is growing, and would be expected to grow vigorously. They will need to be pulled out and kept under control in the future, confined to a specific area of the flower bed if you do not wish them to intrude on other plants. In this case, you need both to pull them out and prevent seeding of the ones that are in the wrong place. This would mean deadheading the blooms as soon as they start to wilt and before the plant sets seed.

The Black and Blue sage is a perennial, which means it will come up ever year from the roots, which will continue to expand, and also to prevent it from seeding.

In the case of the lilies, it would seem they just lost the battle for territory, or perhaps are not well-adapted to the soils and climate of your area.