Thanks for your reply, Maverick.
The following screenshots are specifically for the lifetime score variable, which simply is the sum of all the scores the player has ever had ever.
I started with a specific Event Sheet for the saving, which I included in the playing level layouts, as shown below.
As I at first thought it was outright not saving anything, I also added it specifically in the levels, when the game over menu is displayed, right after the score has been added to the lifetime score, as shown below.
As I mentioned before, all of the global variables work and the localstorage does ultimately save, but it takes too long doing so.