An exact search for L* Besterman, born within the time parameter of 1930 +/-5 years turned up only Lajb Besterman. In addition to the minor variation on spelling in the first name, Lajb was also born in 1927, which would have made him the right age to have attended School #13B.
I found multiple people who lived at the same addresses as Lajb. He lived with his father (Mordka, b. 1888), his mother (Estera Rywka, b. 1891), and his siblings Moses (b. 1922), Zyskind (b. 1925), and Majta (b. 1930).
There is no information listed regarding the fate of either Estera Rywka or Zyskind. Moses was deported on September 12, 1942, on which date there was a deportation to Chelmno. Mordka died of currently unknown causes on May 3, 1942. Both Majta and Lajb were deported on September 29, 1942, but there is no deportation listed in Secondary Sources associated with that date, so at this point theeir fate remains uncertain.