(It's been a while since I read the book, but I believe this the answer.)
Annemarie meant that since her best friend (Ellen) is Jewish, Ellen had to come hide with Annemarie and Annemarie's parents. Ellen also had to be called "Lisa", or the Nazis will have the ability to identify Ellen and take her away to the concentration camps. With the portrait of dark-haired Lisa, Ellen managed to keep the disguise before she had to be transported to Sweden.
