Although he's named after Lulu's husband, Henry Lamartine Junior is actually Beverly's biological child—Bev and Lulu had a fling the day of Henry's funeral, and Henry Jr. arrived a few months later.
Beverly sells learning guides for a living, even though he isn't the sharpest or most educated knife in the drawer (but really, can a knife be educated?):
Door to door, he'd sold children's after-school home workbooks for the past eighteen years. The wonder of it was that he had sold any workbook sets at all, for he was not an educated man and if the customers had, as they might naturally do, considered him an example of his product's efficiency they might not have entrusted their own children to those pages of sums and reading exercise. But they did buy the workbook sets regularly, for Bev's ploy was to use his humble appearance and faulty grammar to ease into conversation with his hardworking get-ahead customers. They looked forward to seeing the higher qualities, which they could not afford, inculcated in their own children. (5.1.18)
So, he totally used his humble academic background to his advantage—pretty crafty, if you ask us. Also, he would often talk about his own son to help butter up his customers and convince them of his commitment to education—what does it matter that he had no actual relationship with Henry Jr.?
He eventually decided that he wanted to go back to Lulu and take Henry back to the Twin Cities with him (where he lived with his wife, Elsa). Instead, he ended up marrying Lulu and staying. Which, yes, makes him a bigamist (when Lulu discovered the double marriage, she made him go back and end things… and it's not clear that he ever came back for good, actually).