Out of universe (according to her biography Goddess of Love Incarnate: The Life of Stripteuse Lili St. Cyr.) her inclusion was an homage to Richard "O'Brien" Smith's adolescent obsession with all things kitsch and glam.
The wording of the song 'Don't Dream It— Be It' (and presumably much of the rest of the film) evidently contains multiple in-joke references to obscure 1950s burlesque magazines.
Growing up in New Zealand in the 1950s, Richard Timothy Smith's
"adolescence was swamped with joys that most of the fifties decent
society decried as mindless, comics, rock-n-roll, B-movies." He
became fascinated with comic books and pulp fiction, in his town of
Tauranga was a shop filled with kitsch and magazines. Lili St. Cyr.
adorned many of those magazines.
Smith became fascinated with her. She "was one of the most beautiful
women in the world and, by default, a transsexual's dream girl." Smith
noted that burlesque "was aimed at the eternal adolescent in males."
Lili clearly was the leading element of that "particular Zeitgeist."
In 1973 Smith, now known by his stage name of Richard O'Brien, wrote
what would become the cult hit The Rocky Horror Picture Show, both the
musical and, in 1975, as a cowriter, the screenplay.
The character Janet, played by Susan Sarandon in the film, sings
"Don't Dream It— Be It." It was inspired by one of O'Brien's pulp
magazines asking the question, whatever happened to King Kong actress
Fay Wray? The last line of the song is "It's beyond me, help me,
Mommy — God bless Lily [sic] St. Cyr." And though it was just
twenty-five years from her heyday in the fifties, most of RHPS's
audience had no clue who Lili St. Cyr was. The "inclusion of Lily
[sic] was driven by the recognition of my own imagined self."
O'Brien believes the LA stage version bought some of their costumes
from Lili's lingerie store in 1974.