Instead of spray-killing a lawn or manually removing sod, stress the lawn area by repeatedly scalping and dethatching over a year. In fall, overseed with grasses and flowers of your choice. You can even bring in potted plants or plugs to create drifts, masses, tiers and levels of perennials, shrubs and trees to create design focal points and give slower-to-establish plants a leg up. Over time your seeded plants will begin to overtake the older lawn, particularly if you have some more aggressive species in there.
Tip: Consider planting some annuals and biennials as temporary cover crops while perennials germinate and become established. Black-eyed Susan (Rudbeckia hirta, zones 3 to 9) and upright prairie coneflower (Ratibida columnifera, zones 3 to 9) are personal favorites, because they tend to diminish in a few years, about the same time new perennial flowers and grasses gather steam. The benefit of these early nurse plants is not only that flowers are made more immediately available to pollinators, but that they will help compete against weeds and start amending the soil with their roots.