I used the Lodz Ghetto Inhabitants database to do a "Fuzzy" search for all inhabitants with the name "Erlich" and looked through 590 records. The two "siblings" and the "Mother" Chaja all shared the same address for Tema. I have had no luck thus far finding any information on the father, however I have a lead for "Ignacy Erlich" that will require further research.
According to the JewishGen.org's Lodz Getto List results 101-150 (searching for last name "Erlich"), Temer (alternate spelling of Tema) died at the Lodz Ghetto on 20.05.42. Since Temer and Tema have the same DOB, address, and occupation (student), I believe this to be the same person. (http://data.jewishgen.org/wconnect/wc.dll?jg~jgsys~allcountry2)
Chaja D. Erlich died 7/17/1942 according to the Lodz Hospital Death Records (Document Control # 7269, Pg. 11) from Lungentuberkulose. If Chaja was the mother of our Tema, it is likely she passed from the same illness.