Haven't heard of Luke Swick, born circa 1800 in NJ, but might be able to narrow to possible parents.
Johannes and Barbara Swick, the progenitors of the New Jersey Swicks had 5 sons, who all lived, at least early on in Somerset, Hunterdon and/or Sussex Counties, New Jersey. By 1800, John had died, and Martin, Peter and Tunis were past their reproductive years and/or known not sons that young. I have seen no record of Bergon, the youngest, and assume he died in the American Revolution.
John had two sons. The eldest, also named John, born 1755-1763, presumably stayed in Hunterdon County and might be a father or grandfather of Luke. The other, Tunis C., probably left migrated from NJ to NY before 1800.
Martin had several sons old enough, but moved his family to Pennsylvania before the American Revolution.
Peter Swick was settled in Hunterdon County, NJ, until around 1800, when he migrated to Northumberland County, NJ. He had 3 sons who could be Luke's forebear. John, born 1770, later migrated to Licking County, Ohio. Peter, born 1772,migrated to Ontario in 1810. Martin, born 1776, migrated to Richland County, Ohio, after 1800, and wss known to have 8 children (don't have any names).
Tunis Swick was settled in Hunterdon County, NJ, and had moved his family out of NJ before 1800.
Bergon Swick had no known issue.
A good general source is to google Dennis Swick' genealogies. He has a lot of stuff.