Lawrence's real name should have been Chapman, as his father was an Irish landowner in co. Westmeath and who was to inherit the Chapman baronetcy. But because father had all Chapman daughters, and all his Lawrence sons were illegitimate the baronetcy became extinct on his death.
The Chapman family arrived in Ireland with the 16th/17th Munster Plantations, having it is believed originated in Devon. My above titled book published in 2000 attempts to detail all this, and convincingly puts straight the family legend that it was descended from Sir Walter Raleigh, though it was distantly related.
This is an A5 size paperback, of 153 pages, plus 8 pages of b/w illustrations, with colour covers. Extensive Bibliography.
Although out-of-print, it may well be obtainable on the internet.