Lilith knew that Eve would not make it. At least not at the first time. Eve would rather play the roles dictated by the norms, living within the limits, than questioning anything.
Meeting with the snake was an option to break through into freedom but she was not ready.
Lilith saw it before it happened. She had the vision. She knew that she had the free will to choose and in order to break free, she had to risk EVERYTHING. She knew she had to face the darkest part of her own, and she had to go down to Hades to get the key to open doors or to open that sacred book of Knowledge. The Thoth.
She knew the legends how that book took lives and brought suffering to everyone who was not prepared and who wanted to control it or who tried to get a hold on the Sacred Serpent, who guarded it.
The key was connected with the Serpent, as she was connected to it as well. She needed to find that language on her own to spell the Name. She needed not only face the snake but to be able to surrender and become one with it.
Eve did not know the language... do you?
Say the name and the Serpent will awaken and will form two spiraling grooves around each other and will raise higher and higher to the gland. Say it and the connection will be made.