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Unfortunately, to restore your Federal rights, you need to restore your state rights in the state that took your rights away from you. You're unfortunately correct that Texas will not expunge a conviction unless it's first been pardoned by the governor. So you're going to need the governor's pardon in order to get your rights back.
Pardons are not easy to get, but if you do, the Federal and state government will lift their bar and that should also be sufficient for Louisiana to let you get a gun.
Any former offender can apply for a pardon without the need of a lawyer. This is a link to an instructional booklet so that you can see what it entails. Once you are pardoned you can apply for an expungement, though you wouldn't need it to get your gun rights back in full.