There appear to be at least 5 authors published under this name.
1. Elizabeth Lawrence (1904-1985) wrote gardening books.
2. This Elizabeth Lawrence is a cookbook editor and author connected with the NYT.
3. Elizabeth Lawrence is a children's book illustrator published in the 1990s -2000s.
The Open Door books are children's education books co-authored with Noreen Wetton. 'It Had to Be Us' is possibly a self-published memoir. Further research is ongoing.