It is very difficult in that time period to determine if there was one John or two. If he were born later, you'd find him in census records, either living with his mother and stepfather or sometimes with his grandparents. I think sometimes stepfathers didn't want to claim children from previous marriages. Or maybe the grandparents needed help form their grandchildren, who knows? It was also very common for stepchildren to use their stepfather's LNAB and to revert back and forth between the names.
In this case, since you cannot find anything for the LNAB of Browne, I think it is very likely that he was John Lumbrozo, he was mentioned in the will of his stepfather, and you should change the name. You should include details in the biography explaining why you think the name is Lumbrozo and what steps you took to determine that. You can state where you searched and what you searched for.