I am having this same issue… My Site Health status shows:
“The scheduled event, lh_wayback_machine_single, failed to run. Your site still works, but this may indicate that scheduling posts or automated updates may not work as intended.”
I have disabled every other plugin I have and enabled LH Wayback Machine… updated a post and it still shows as Queued.
I also deleted the LH Wayback Machine plugin and reinstalled with no other plugins active and it did the same thing.