It is important to note that there were two Estera Lachman's who could have signed this book. In the database, there was an Estera Gitla Lachman and an Estera Lachman. Estera Lachman's birthday falls one year outside the range of likely birthdays for students attending this school, but it is still possible that she could have signed this book.
Estera Gitla Lachman was born on 12 Sept 1929, and lived on Cranach and Scharnh streets. Estera Lachman was born on 8 Jul 1933 and lived on Hohens and Wolczan streets.
Chaim Hersz, Chana Rachel and Nachem are Estera Gitla Lachman's mother, father, and brother. I was able to identify them because they shared the same street addresses as Estera Gitla.
I was only able to find Estera Lachman's mother Liba. I found her because Liba and Estera Lachman shared the same addresses.
On JewishLodzcemetery.org, I was able to find graves for "Estera Lachman" as well as "Gitla Lachman". This could be one of or both of the girls, but all I was able to find was their names. Unless I was navigating the site incorrectly, I could not find when they died, all I could find was their names.