This is a grass type Liriope Variegated
Variegated Liriope
Botanical Name: Liriope muscari 'Variegata'
Sun Exposure: Full Sun, Partial Shade, Full Shade
Height/Habit: 8 - 18 inches
Spread: 12 - 18 inches
Spacing: 12 - 18 inches
Hardiness Zone: 5-10
Flowering Date: Mid Summer to early Fall
Winter Care: No winter care needed.
Growth Rate: Slow
Flower Color: Purple
Flower Form: Spike - tiny grape like clusters, 4-8" long, similar to those of the Grape-Hyacinth
Foliage Type: Grassy-leaves striped lenghtwise of green and creamy white.
Resistance: Deer Resistant
Soil Requirement: Moist well drained soil.
Watering Requirement: Moist well drained soil. Once established it is drought tolerant.