Would appreciate some direction on this family who came to America, supposed between 1903-1906. I wasn't sure which 'county' board to post on, so I've posted here.

According to passport application and other sources,

George (Americanized?) Peter (Frederick) Gormsen was born July 14th, 1884, then son of Hans Peter Gormsen (who George says was still living in his 1921 passport application) and Louise Lehmann in Lunghoi (Lunghoj?), Denmark. According to his census' between 1910-1930, he left Denmark between 1903-1905, but I have not found any immigration ship manifest with his name, so I'm not counting that info as proof. He did become naturalized, and I will be getting that info.

His wife (who also came from Lunen Island to meet him in the US) was Laurentza Miller-Hansen, born August 31, 1886, the daughter of Frederick Miller and Amalie Hansen. I have yet to find either ship these two sailed to make their way to the US.

Would greatly appreciate confirming documents from Denmark or suggestions on the best sources to find said documents.
Thanks.