Ask Mr. Smarty Plants

There shouldn't be any problem with raised beds over lateral lines; in fact, the moisture from the lines will probably benefit the plants you choose. When you say you wish to plant "perennials," your concern needs to be more with the roots of the desired plants. We usually recommend grasses to go over lateral lines, because they have fibrous roots that will not interfere with the lines. However, we assume that what you want are herbaceous blooming perennials. What you need to avoid are perennials that become woody, with extensive woody roots, which will interfere with the lateral lines.

From our Native Plant Database:

"Fragaria virginiana (Virginia strawberry), native to Arkansas,  is a ground-hugging plant rising from a fibrous, perennial root system. Hairy leaf petioles, up to 6 in. long, each bear a single trifoliate leaf. The hairy flower stalk gives rise to a loose cluster of small, five-petaled flowers followed by tasty, wild strawberries. Found in patches in fields and dry openings, this plant produces the finest, sweetest, wild strawberry. The edible portion of the strawberry is actually the central portion of the flower (receptacle) which enlarges greatly with maturity and is covered with the embedded, dried, seed-like fruit."

Cultivated strawberries are hybrids developed from this native species and the South American one. The Lady Bird Johnson Wildflower Center is dedicated to the use, propagation and care of plants native not only to North America but to the area in which they are being grown. A hybrid, which is probably what you intend to use, falls outside our expertise. However, we are going to assume that the cultivar (cultivated variety) will also have fibrous roots and therefore be appropriate for planting over your lateral lines. 

We will go to our Recommended Species, click on Arkansas on the map, and then select "herb" (herbaceous blooming plant) under GENERAL APPEARANCE and "perennial" under DURATION. From this, we will try to select plants that do not become woody as they mature and that would be useful in your garden.  We do not intend this to be a list of plants you must use, but only indications of the kind of plant we recommend you use. You can make your own selections, using this same method, inserting specific site requirements for sun exposure, soil moisture and so forth.  Follow each plant link to our page on that plant to learn the expected size, bloom time, etc.

From our Native Plant Database:

Fragaria virginiana (Virginia strawberry)

Aquilegia canadensis (red columbine)

Callirhoe digitata (winecup)

Coreopsis lanceolata (lanceleaf tickseed)

Echinacea purpurea (eastern purple coneflower)

Monarda fistulosa (wild bergamot)

Oenothera speciosa (pinkladies)

Ratibida columnifera (upright prairie coneflower)

From our Native Plant Image Gallery:

Fragaria virginiana

Aquilegia canadensis

Callirhoe digitata

Coreopsis lanceolata

Echinacea purpurea

Monarda fistulosa

Oenothera speciosa

Ratibida columnifera