There seem to be two Elizabeth Vincent Fosters: one, the author of Gigi, died in 1963, and was born in 1905. Gigi is a merry-go-round horse, whose mother was a pine tree and whose father was the wind that sweeps through the Vienna woods. Gigi, perhaps not surprising when you consider his parentage, has adventures. Both Gigi, and its sequel, Gigi in America, are easy to find though more so in America, where the books were originally published.
The Elizabeth Vincent Foster who wrote Lyrico I think is someone completely different, as Lyrico is her first book, and it was written in 1970. Perhaps she is a relation of the original Elizabeth. Lyrico is the story of Philippa, who longed for a horse but lived in the city. Then she is sent a horse; of an extremely rare breed, which happens to have wings. The book is easy to find in paperback; a little less so in hardback.