Old W-2's can't be amended because the withheld taxes have long since been deposited with the state. The old W-2's reflect what the employer actually withheld and deposited, so they in fact are correct. The normal recourse for a taxpayer who's been taxed incorrectly is to seek a refund of the incorrect withholdings from the state.
A Louisiana non-resident who performed no work within Louisiana, not even for a single day, has no tax obligation to the state of Louisiana for his work income.
Here are a couple of supporting citations from the Louisiana revenue code (https://revenue.louisiana.gov/LawsPolicies/LAC61_I_1304.pdf)
D. Compensation of Salaried Employees with a Constant
Rate of Pay. The Louisiana income from personal services is
the proportion of total compensation from services rendered,
which the total number of working days in the state bears to
the total number of working days both within and without
the state.
If the number of working days in Louisiana is zero, then the proportion of total compensation that is Louisiana income is zero.
Also, from the same source:
"Income from sources within Louisiana
includes compensation for personal services rendered within
Louisiana."
By implication, compensation for services rendered outside Louisiana is not Louisiana source income.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
