I did a search for L* Szymkiewicz, and narrowed the results down further to those that had been born +/- 5 years from 1930. Laja was the only result that was a female, and this led to me deducing that she was the student that signed the album.
I matched Laja to her family by observing the same patterns of addresses and moving dates amongst people of the same last name. I found who is presumably her father (Chaim, b. 1897), mother (Szajndla Sara, b. 1893/1906), and brother (Zalma, b. 1923). All four moved on February 22, 1942 and lived at both Krautergasse and Inselstrasse. Since I found Chaim's birthplace listed as Kalisch on his death certificate, I presumed that Kalisz was the place of birth of Laja.
I think I found Laja's labor card, although the year doesn't exactly match up. The only other Laja in the Lodz Ghetto databases was born in 1912 and I assumed that this Laja was a closer and more probable match. Also, the death date matches up with that in her profile.
There is no information listed regarding Zalma's fate. Chaim died on July 27, 1942 of malnutrition. Szajndla died on August 2, 1942, and Laja died on April 7, 1944, both of unknown causes.