I don't think there is another murder committe by Walt in the show's run where the reasons for the killing are not quite clear. I sure hope someone asks Vince about this.
Interesting; like I said I thought the "why" was quite clear. Why did Walt go back to Albuquerque? Because he thought he'd come up with a way to provide for his family. Lydia was a fearful, almost paranoid individual with ready connections to killers, no compunctions about using them, and a lot of motivation to do so. Going to the lengths he went to with the money but not addressing that very real, life-or-death threat doesn't seem very likely for thorough old Walt.
I don't disagree with anything you write above (except the "clear" part). My argument isn't that Walt had no reasons to kill Lydia.
In "Granite State" we see Walt try to get money to Junior and throught the series Walt tells us that the money he makes is for his family. We then see Walt go back to Albuquerque in Felina and do just that.
Also in Granite State, Walt tells Saul that he wants to kill Jack for what he did to Hank. Walt then returns to Albuquerque and does just that.
What we don't see is Walt making the decision to kill Lydia. We the audience see that Lydia should be on Walt's hit list because among other things, she wants to see Skylar dead.
But we don't ever see Walt find out that Lydia has recommended to Todd that Skylar be killed and then Walt deciding to kill Lydia. Essentially, all we are actually shown is Walt killing her.
The show rather meticulously had Walt tell us, or show us his reasons for killing Jack and pretty much everyone else he has killed, but shows almost nothing of his reasons for killing Lydia.
Again, not arguing that he had no reason to kill Lydia, and if you want to go with the "for the protection of his family" angle, I would not blame you. Personally, I'm going with the ego/legacy reason because that is the one that I think was kind of shown on screen.
Where is the scene that shows us Walt deciding to kill Lydia and his reasons for the decision?