Strawberries are vigorous growers, producing new plants that form from long runners. The plants have a dense, compact form that would compete with any other plant for sun, water and space. Tiger lilies grow to 4 feet high on long, somewhat spindly stems. Planting strawberries with anything but strawberries will likely result in frustration, unless you are growing strawberries more for their ornamental value than fruit. They may spread by several feet every season, requiring constant pruning to keep them in bounds when placed amid tiger lilies.
Strawberries require annual renovation to keep them healthy, which involves mowing the leaves in the fall and digging up and discarding new plants to narrow the plantings. Mowing strawberries planted with tiger lilies would likely be very difficult and would probably damage the lilies. Strawberries need more water and fertilizer than tiger lilies, and although tiger lilies tolerate full sun, their blooms will look better in filtered shade.
If you're determined to plant strawberries with tiger lilies, select day-neutral strawberries that don't produce many runners. Plant one or two plants only and prune them back to keep them from spreading. Another option is to grow the strawberries as annuals, replacing them every year.
Plant strawberries by themselves in containers, strawberry planters or even a raised bed in the garden if you have space. Renovate them yearly and provide frequent applications of fertilizer, mulch and water. Plant tiger lilies alone or with other perennials and shrubs in a mixed border. Plant shallow-rooted, non-invasive, small plants around tiger lilies to cover their spindly foliage. Try annuals, such as petunias, or perennials, such as hostas, ferns or day lilies.