This summary is not the rule. The rule text controls.
Here's a plain English summary of this rule:
When a case goes to a Louisiana appeals court, the court generally only looks at the specific issues that were already argued in the trial court and that the person appealing has clearly listed as problems (called "assignments of error"). The appeals court is not meant to search the whole case for new issues on its own. It focuses on what the parties raised and asked it to review.
There is one exception to this. If the court believes that justice requires it, the court can look beyond the listed issues. This gives judges some flexibility to fix a serious problem in a case, even if nobody specifically pointed it out on appeal.
For someone involved in a case, this means it is very important to raise every issue you care about at the trial court level and again clearly in your appeal. If you skip an issue or fail to list it as an error, the appeals court will likely not consider it, unless the situation is serious enough that the court decides to step in anyway.