I have Ajuga growing in similar conditions but it tends to want some water to look it's best. It will be below the mower blade too.

My spearmint gets almost 12 inches tall and goes dormant without water.

Texas betony (Stachys coccinea) should work there and stay green all year. The native golden columbines (Aquilegia chrysantha var....) should also do well and remain semi-evergreen.

Here is a link that might be useful: Stachys coccinea

Phox pilosa , shrimp plant , iron plant, Greek pattern plant. wandering jew, lirope , salvia roemeriana,scuteleria ovata, agave braceosa, sago palm ( it will need fronds trimmed off after a freeze).

This post was edited by wantonamara on Mon, Jan 19, 15 at 10:53

barbed wire! (to repel those mowers!)

Excellent suggestions--thanks!