Many historians, such as Massie, mention that Lenin may have abruptly become ill in 1922, and died two years later, because he was poisoned. However, nobody ever mentions why this is thought, who may have done it, or what poison was used. Could someone explain what evidence is used to support the theory of Lenin's death by poisoning?
It's hard in history to prove that something did not happen, which is along the lines of the "impossible to prove a negative" concept. However, I think most historians do not believe Lenin was poisoned.
This article is a nice and quick write-up of the issues Lenin dealt with, which included infections and an assassination attempt. Beyond being a megalomaniac, he was also a workaholic and forming a government that was under siege from all sides, yet trying to revise almost all aspects of Russian life. Given the standards of health care for Russia in this period, Lenin's medical history, age, work habits and a guess at his stress levels, it's not surprising that strokes hit him when they did.
The article above also provides a bit of conjecture about the poisoning scenario but I think it is simply conjecture. The article talks about the rivalry between Lenin and Stalin, but I believe a lot of historians misconstrue it.
When Lenin's strokes started to occur, it sidelined Lenin who would have otherwise been front and center in all decisions. This created a large power vacuum that had to be filled if the Soviet movement was to put the civil war in the bag and move on. The vacuum had to be filled and Lenin didn't want anyone else to fill it, and so he chafed when moves were made to fill the void without him. I believe his Testament was to lash out at those who were closing out his involvement with the government and to still exercise the control he was used to wielding.
Also, Stalin at this time was not one of the central figures in the Party or government yet, although he was an up-and-comer. I don't think Stalin would have made such a move against Lenin either - Stalin didn't have the coalition to challenge Lenin while Lenin was alive and had such a plot been discovered, he would have had no effective coalition to save himself. Stalin didn't assemble the ruling coalition as we know Stalin's regime today for several years later after Lenin's death.