Hugo Lewi traded in military surplus
Unlike the Kleemanns, the Lewi side of the family had few relations in Danzig. That's because Hugo came to Danzig from another German region, Thuringia, and his family roots are in the town of Sondershausen. We know he married Emilie Kleemann in 1870, and that their five children arrived in quick succession.
The Danzig address books show an interesting tidbit about Hugo's line of business that does not appear in the Sue Key book. He traded in "military effects," which may be items such as swords and uniforms for collectors or surplus. The Prussian military tradition ran strong in Danzig, which must have made for a business opportunity for Hugo Lewi.
The three listings are for 1874, 1886 and 1896. He was not listed in either 1869 or 1905, which gives an idea of his years in Danzig. Hugo, Emilie and all the Lewis relocated to Berlin sometime after 1996. Hugo died in Berlin in 1909.
The mention of "Eisner nachfolger" in each listing means the firm is a successor to a previous company. This suggests that Hugo purchased the business from a previous owner, Eisner. I'll take a look at earlier address books to see if I can find an Eisner in the military effects business.
One other term in the listings is not fully clear to me. "Herren-Garderobe-Magazin" translates as men's wardrobe storage, which sounds like another kind of business but not especially related to military effects. Maybe the storage was for military uniforms.