Your book was likely "The Dream Watcher" (1968) by Barbara Wersba.
" The main character, the boy, doesn't fit in at home or school... He
meets an old woman who is manifestly eccentric, and claims to be a
retired actress, who once knew Sarah Bernhardt. She helps the boy
learn to be himself. Its only when she dies that the boy finds out she
was nuts.. she was making up her entire life, whole-cloth."
From The New York Times review:
"The Dream Watcher is the story of Albert Scully, a high-school boy...
It is also the story of Orpha Woodfin, a marvelous old nut...
Miss Wersba has bravely undertaken the difficult stylistic
accouterment of much quoted material from Shakespeare...
The old lady, living in the only remaining original house in the
midst of a new development, bills herself as a bygone actress who once
The New York Times, November 3, 1968, p. 469
Vintage copies available from Abebooks.com starting at $1.94.
abebooks, advanced search terms: old lady fiction (1965-1975)
I hope this helps.