If you have any old LRTimelapse version installed, trash it, empty trash.
In this Process new, perhaps due to the switch from LRT 5 to LRT 6?
In the past the guideline has been: If you have a former version of LRTimelapse 5 installed, there is no need to uninstall first. Just run the new installer

Do I have to make any manual Backups for getting all my edited content still in place during the update Process to LTR 6 in Case of deleting LRT 5 at first?

No, this is just to make sure there are no old icons from LRTimelapse 5 around since you cannot use LRT5 and 6 in parallel.
Nothing to do with your edited content, just the LRTimelapse Application itself.