The little bit of Anakin that was left inside him wanted to keep his son from falling into darkness, so he refused to let Luke kill the Emperor -- even though he would have loved nothing more than to have Palpatine dead. When Vader instigated the duel, Luke naturally fought back.
Luke tossed his lightsaber to show that he is not being drawn to the violent angry Dark Side path that Palpatine was trying to push him into. We can speculate that Luke didn't think that Palpatine would need to fight with Palpatine.
Darth Vader's deep hatred for Emperor Palpatine grants him power, but also inflates Palpatine's importance in his life, making him impossible to kill. In Vader's latest adventure, it is implied that he hates Palpatine more than himself, recognizing him as the most important thing in his universe.
"With your hatred you will take my life," Palpatine commanded his granddaughter Rey in Rise of Skywalker, "and you will ascend." That was why the Emperor taunted Luke all those years earlier, intending the Jedi to kill him in anger and thus fall under his influence.
Did Vader want to overthrow the Emperor with Luke?
Despite Vader's seeming loyalty to the Emperor, Palpatine wanted to replace his servant with a new apprentice, while Vader plotted to overthrow the Emperor so he could rule the galaxy with his son. In the end, Luke surrendered himself to Vader on the forest moon of Endor.
Why Vader Stopped Luke From Killing the Emperor (Not Why You Think) - Star Wars Explained
Why did Vader stop Luke from killing Palpatine?
Vader's redemption in Return of the Jedi was not just about saving his son; it was also a defiance of the dark side's corruption and his own past as a Sith Lord. Vader's decision to block Luke from killing Palpatine was motivated by his knowledge that it would corrupt Luke and lead him down a similar path of suffering.
Return of the Jedi, however, proved that Palpatine had a significant blind spot. There were plenty of warning signs Palpatine could have heeded that Vader might turn on him, and yet his ignorance and arrogance led to his decisive downfall.
But beyond that, Palpatine's plan was three-fold; first, he wanted Kylo Ren to kill Rey when he found him on Exegol. Then he wanted Rey to strike him down and absorb the spirits of all the Sith.
He often refers to Vader as a tool that can be discarded when he is no longer of any use, and yet still Vader obeys. Despite wanting Vader to obey, Palpatine still sees his apprentice as pathetic and someone who could never surpass him.
Vader's innate talent with the Force would have made him more powerful than Palpatine, if not for Palpatine meddling in his life from a young age. As it stands, Palpatine's influence over Vader was too great for Vader's strength to overcome, forcing him to take Palpatine down when he was prone and unaware.
The light side is said to be stronger than the dark, but Palpatine's connection to the Force appears to have grown far stronger in Return of the Jedi. So while Luke may have bested him in terms of athletics, Palpatine's Force-powers could very likely give him the victory.
With that being said, if Palpatine did, indeed, use Force-healing to keep Vader alive, he didn't appear to have given enough life force for it to take a toll on him -- and being as close as Vader was to death, Palpatine would have required a lot of energy to keep him alive.
Vader had no idea he had been groomed by Palpatine his entire life and that their friendship was entirely fake. He still believed Palpatine was telling the truth when he said he would help save Padme. So, from Vader's distorted point of view, Palpatine had done nothing wrong and was the only person left by his side.
Star Wars Legends, specifically the novel Dark Lord: The Rise of Darth Vader, explained that even though Vader was capable of killing the Emperor, he wasn't in good psychological condition to do so.
Instead, she deflected his lightning, darkness, and anger back at him, using the strength of Jedi long gone to allow her to hold on for as long as she needed to. Rey managed to beat Palpatine not necessarily because she was stronger with the Force, but because she knew his rage would get the better of him eventually.
So when Rey reappears as an adult after her awakening with the Force, Palpatine simply sent Kylo Ren to eliminate her because Palpatine no longer needed her, and she constituted a threat to him.
Only after locating the zombie-like Palpatine on Exegol in the opening sequence of The Rise of Skywalker does Kylo discover the truth. Revealing his behind the scenes machinations, Palpatine hints at the truth of Rey's bloodline, and Kylo asks to know more.
He understood he lost the ethereal battle before their physical fight even began. Thus, Palpatine never viewed Yoda as a major concern, even though the Jedi Master fought him to a de facto draw during the events of Revenge of the Sith.
Palpatine used his powers to hide his true nature from the Jedi, utilizing Force Concealment to completely hide his presence in the Force while clouding the Force for the Jedi. The Clone Wars also kept the Jedi busy and weakened, preventing them from realizing his true identity.
