Is not informing a friend about opening the page—after telling her it wouldn't be opened—considered a lie that necessitates sin?

If your intention by telling your friend that she has not yet opened it was about deactivating the account, then this is not a lie. A Muslim should be keen on truthfulness, and it is permissible for him to use allusions (ta'ridh) and equivocation (tawriya) when necessary. As Imran ibn Husayn said: "Indeed, in allusions there is room to avoid lying," and Umar ibn al-Khattab said: "Is there not in allusions what suffices a Muslim from lying?"