The Norwegian royal family will be represented by Princess Astrid at the funeral of Princess Lilian of Sweden in the Palace Church in Stockholm on Saturday. The King and Princess Lilian were fond of each other, but the King will attend a skiing event that day (it is not the first time he makes sporting events a priority above family funerals).
The court of Copenhagen has not yet announced who will represent the Danish royal family, but given that Princess Lilian was the aunt (by marriage) of Queen Margrethe I would not be surprised to see Queen Margrethe herself and/or her sisters.
As this is a considered a smaller event than Prince Bertil’s funeral in 1997 I would expect that only those foreign royals with a personal connection to the late Princess will attend, which might mean only the Scandinavian royal families (although Prince Philip of Britain was fond of her).
At the funeral of Prince Bertil, Norway was represented by the King and his two sisters with their husbands, Denmark by Queen Ingrid, Queen Margrethe, Prince Henrik, Princess Benedikte and Prince Richard, Britain by Prince Philip, Belgium by Queen Paola, the Netherlands by Princess Margriet, Luxembourg by Grand Duchess Joséphine-Charlotte and Spain by Princess Cristina, if I recall correctly. The President of Iceland and a former President of Finland were also in attendance, which will probably not be the case this time.