From my book, Queen Victoria's Descendants:
"Following his divorce from Princess Christina, Prince Andrej married Princess Kira of Leiningen, the third child of the 6th Prince of Leiningen and Grand Duchess Maria Kirillovna of Russia, and yet another descendant of Queen Victoria.
Kira and Andrej were married in September 1963, but the announcement of their marriage was not made until after the birth of their first son, Karl Wladimir, the following March. A second son, Prince Dimitri, was born a year later. A few months after Dimitri's birth, Prince Andrej and Princess Kira adopted a four-year-old girl, Lavinia Maria, who was, in fact, Kira and Andrej's natural daughter, born in 1961 when Andrej was still married to Princess Christina. The adoption was a formality to give the little girl a new surname. Crown Prince Alexander, as Head of the Family, has recognized Lavinia as a Princess of Yugoslavia.
and from one of the footnotes:
Lavinia Maria Lane was born at 12 Avenue Road, St. John's Wood, London. No father's name appears on her original birth certificate; her mother's name is given as Kira Lane. She is the natural daughter of Princess Kira of Leiningen and Prince Andrej of Yugoslavia and acknowledged as Prince Andrej's daughter. After the couple's marriage, Lavinia was adopted by her natural parents to avoid a scandal within the family. The adoption became official on November 15, 1965. Kira Karageorgevich, late Lane, formerly Leiningen is the name listed on Prince Dimitri's birth certificate. Both Dimitri and Lavinia were born at l2 Avenue Road, while Prince Karl Wladimir was born at the Royal Northern Hospital, Islington. HRH Crown Prince Alexander of Yugoslavia, as Head of the Family, has confirmed that Lavinia Marie (the middle name was changed from Maria to Marie in the adoption because of a misprint on the original certificate) is entitled to the style and title of HRH Princess of Yugoslavia.
Thus, Lavinia is recognized as a member of the Serbian royal family as HRH Princess Lavinia.