This looks like someone has wrongly "Frenchified" the English surname Lathrop. Lathrop doesn't occur in my immediately available surname dictionaries, though I found a reference to it on the web which says it is from a village in Yorkshire called Lowthorpe. "Thorp" and "Throp" (the former Norse, the latter Old English) are common elements in English place names that meant "outlying farmstead", so I would think the theory that Lathrop is from an English place name is likely to be correct.
"La Thrope" wouldn't be the first example of a name that has been wrongly respelled as if it came from another culture. There are many people in the USA with the surname "O'Dell". This comes from people wrongly interpreting the English surname Odell
(which is also from a place name) as if it were an Irish surname, which it is not.