My grandfather was Edvin Enborg (1902-1990); his father was Carl Enborg (1866-1954). My great grandfather Carl changed his name to Enborg when he went to Canada for a few years.
I think maybe your Lauritz did the same; changed his name when he emigrated. This was quite a common practice among Swedes with patronymic names.
There is no Erik Enborg in the 1890 Swedish census. The name is quite unusual. And also no Lauritz (or indeed any name beginning with an L) Enborg in the Swedish emigrants records, save for a L Enborg, age 32, who went from Sweden to Boston on Oct.9, 1896. This could be your man. His homeparish in the Swedish records is given as "US", meaning that he has been to Sweden to visit, from the US, and is now returning.
Maybe you can check passenger arrivals for Boston for October 1896. That could be something.