Franziska Sibylle Augusta was born in 1675 at the Schloss Ratzeburg the second daughter of Julius Francis, Duke of Saxe-Lauenburg and his wife Countess Palatine Maria Hedwig Augusta of Sulzbach.
In 1676 the family moved to Schlackenwerth in Bohemia where she and her sister spent their youth. Her older sister Anna Maria Franziska of Saxe-Lauenburg was the future Grand Duchess of Tuscany as the wife of Gian Gastone de' Medici future Grand Duke of Tuscany. When their mother died in 1681, their education was entrusted to Countess Eva Polyxena of Werschowitz (d. 1699). Their education was conducted in the art of courtly etiquette in conversation, painting and music, deemed the traditional education for a female in the era. She was also taught by her grand father Christian Augustus, Count Palatine of Sulzbach.
As the two sisters were the only surviving children of the duke and duchess of Saxe-Lauenburg, they were desirable candidates for marriage due to their inheritance which they would be entitled to at their father's death in 1689.
At her father's death, her sister would become the duchess of Saxe-Lauenburg in her own right and would pass the duchy to her children. Their father was apparently poisoned according to court gossip, the culprit allegedly Countess Werschowitz.
With his death, the Lauenburg line of the House of Ascania was extinct in the male line. However, female succession was possible by the Saxe-Lauenburgian laws. So the legal female heir to the throne, Duchess Anna Maria Franziska, and her sister Sibylle of Saxe-Lauenburg fought for the succession of the former, the elder of them. Also Julius Francis' cousin, Eleonore Charlotte of Saxe-Lauenburg-Franzhagen, claimed the succession. Their weakness was abused by Duke George William of the neighbouring Brunswick-Lunenburgian Principality of Lunenburg-Celle, who invaded Saxe-Lauenburg with his troops, thus inhibiting Anna Maria's ascension as Duchess regnant.