The marriage of Lewis and Hannah was recorded in the marriage register of the New Synagogue. According to census records, Lewis was born in 1815/16 in Christchurch, Spitalfields.
I have a spreadsheet version of the NS marriage records which can be easier to use than the database on SynagogueScribes. Both contain the same information.
I have come across the following record from 1816: Moshe ben Nathan married Rebqeh bat Yehuda-Leib (ref. NSM 574). There are no other details, not even a specific date.
This marriage would certainly appear to be that of Lewis's parents. He was named after his mother's father (Yehuda-Leib) and he named his first son Nathan (b. 1841) after his paternal grandfather.