First, if you are using "Check item exists", you don't need "Get" and "On item get".
You can access LocalStorage.ItemValue from the "On item exists" event.
But this should not cause any issues.
Most problems with local storage happen when people don't wait for Set Item action to finish before reading the same item from local storage.
For example - at the end of the level 1 you save some item into local storage and then change layout to level 2.
On start of level 2 you Get the same item from local storage. If you don't wait for Set action to finish before switching to the next layout, then there is a big chance that the item will be read incorrectly.
Another common mistake is when people don't wait for the Get action to finish before trying to access this data.
Get item "HighScore"
Score Set text to HighScoreVar
Use "Local Storage -> On all gets complete" and "Local Storage -> On all sets complete" and "System-Signal", "System-Wait for signal" to properly organize your flow of events.