This credit exists to prevent double-taxation of income (by more than one state).
If you were a resident of Louisiana, and also had income that was taxed by another state, you're allowed a credit based on the amount of Louisiana tax owed on income taxed in both states.
The other state has to allow its residents to claim a credit for Louisiana taxes paid on its return, and not allow Louisiana residents to claim a credit for taxes paid as a nonresident of that state.
Please note that the "net income tax liability" is generally not the amount withheld. This is the amount of tax due to the other state on the other state's return. You may not claim credit for taxes paid to cities or foreign countries. The credit allowed on your Louisiana return must be for the same taxable year for which the tax was paid to the other state(s).