States: Louisiana: Rapides
Two baptismal records for Francis 1799 and Theresa 1801 LYNCH done at a settlement on Bayou Boeuf, but recorded at St. Paul the Apostle Catholic Church show their parents to be Estevan and Estevano [Spanish for Stephen] Linch and Maria [Spanish for Mary] Wollf, grandchild of Patricio [Spanish for Patrick] Linch and Elizabeth Roberts, natives of Ireland, and of Miguel [Spanish for Michael] Wolf and Sarah Xarvier [probably natives of Germany, but not shown].
I see nothing for the other 3 children you name.
Have you looked in the Rapides Archives on-line through RootsWeb Cooperative ? There may be some colonial records posted there that include Stephen Lynch.