BS”D
In terms of a secular Jew being able to write something like that (not that it is really much better than some of today’s less than inspiring Jewish pop lyrics – part of the appeal is that the language is so much better than today’s Ivrit) – keep in mind that the secular Jews of that era were but one generation from their roots bekedusha – and many knew that they were wrong for being prikei oyl malchus shamayim and therefore longed for Yiddishkeit (to which they could not return because, in today’s lingo – it wasn’t cool).
BTW Imber was known for his abuse of alcohol – and he died in chutz la’aretz. He died in New York in 1909 from chronic alcoholism.