The most interesting escapees I saw in a "lawn" was in Oregon in 1997 when I went on a NARGS Winter Study Weekend and drove out to see the home of Boyd Kline, one of the founders of Siskiyou Nursery. As we got close to his place we noticed that the lawns mostly sported patches of purple flowered violets but at Boyd's the patches were pink! On closer inspection we found the "violets" were in fact Cyclamen coum which Boyd said was because the ants "stole" the seed and took it back to the nests which were in the grass!
I saw precisely the same effect at the home of Brian Mulligan, the former director of the University of Washington's arboretum in Seattle. I asked a question of him: did he lime his lawn. The answer was yes.
While cyclamen are not obligate calciophiles (except perhaps C. purpurascens), they seem to do better with a reasonable supply of calcium. In the PacNW, the soils are so badly leached by heavy winter rains that they tend to be calcium deficient, and cyclamen do much better if limed.
Southern Oregon with its semi-desert conditions may be another story.