If the arrest was recent
Start with the county jail
Someone who was just arrested in Louisiana is almost always in a PARISH JAIL run by the parish sheriff (Louisiana uses parishes, not counties), not in a state prison.
Louisiana has 64 parishes, each sheriff running its own jail, and there is no single statewide jail roster; some sheriffs post an online roster (larger parishes such as Orleans, New Orleans, and East Baton Rouge) while many do not.
Louisiana is also distinctive in that many people sentenced to state DPS&C custody are actually held in local parish jails, so the same LA VINE system is the best single starting point whether the person is pre-trial or sentenced.
The reliable paths for a recent arrest are the arresting parish sheriff's jail roster, LA VINE, or calling the jail's booking desk.
Louisiana has 64 parishes (not counties), each sheriff running its own jail and roster (some with no online search); because many state-sentenced people are held in parish jails and there is no unified statewide search, LA VINE (VINELink) is the practical statewide starting point.