I checked the New Orleans Birth Index for you and did not find any Sturlas.This could mean that Lawrence was not born in New Orleans, or that the birth was not recorded by the city.If the family was Catholic, it is possible that the Diocese of New Orleans would have record of his baptism, though.
The census date for 1850 was June 1st, but I don't see a Sturla family in the 1850 census.The only Sturla was an 8 year old girl in New Orleans.I don't see a 9 or 10 year-old Sturla born in LA in the 1860 census either (anywhere in the US).
I did find the 1870 census that lists his birthplace as N.O.I don't think this means New Orleans.In 99.9% of entries, birthplace is listed as a state, country or province of a foreign country.I think it is unlikely that the enumerator would have listed an abbreviation of a city in a different state.
This appears to be your Lawrence Sturla in 1900, and it lists his birthplace as Nevada.
1900 United States Federal Census > Maryland > Baltimore City (Independent City) > Baltimore Ward 24 > District 315 > Page 12A
Dwelling 200/Family 227
1502 Fonson (rents)
Lawrence Sturla, hjead, white, male, b Mar 1850, 50, married for 14 years, b Nevada, parents b ITaly, pilot, reads, writes
Elizabeth, wife, white, b Feb 186,, 34, married for 14 years, bore 6 children, 5 surviving, she and parents b England, immigrated 1879, reads, writes
John S, son, white, b Mar 1889, 11, b MD, reads, writes, attends school
William A, son, white, b Jan 1891, 9, b MD, attends school
Emma T, daughter, whtie, b May 1895, 5, b MD
James P, son, white, b Dec 1897, 2, b MD
Rolond E, son, white, b Mar 1900, 2 months, b MD
Have you been able to find Lawrence's death certificate?This should list his birthdate and birthplace, to the best knowledge of the informant.