Is merchandise purchased while out of state with sales tax paid subject to LA income tax?

It depends, These items would be taxable in LA if:

1. Your out-of-state purchase is for use inside of Louisiana,
2. You were a Louisiana resident at the time of purchase, and 
3. The amount of sales tax you paid is less than the applicable sales tax in Louisiana

If those three conditions exist, you would need to report the purchase on your Louisiana return and then enter the amount of sales tax you paid on the items, to receive the appropriate tax credit.  You then pay the difference on your tax return.

If those three conditions are not met, the purchases do not need to be reported.