Oddly, the Wikipedia page about the Executions has the soviet leadership saying that Lenin didn't have a part in it:
They acknowledged the murders in 1926 following the publication of an investigation by a White émigré, but maintained that the bodies were destroyed and that Lenin's Cabinet was not responsible.
On the other hand, the article mentions Yakov Yurovsky who, I remembered from research I did a few years ago, kept a diary in which he captured the events of that night.
So I looked up his Wikipedia page where it specifically implicates Lenin in the executions:
It has been documented that the order to assassinate the Imperial family came from Yakov Sverdlov in Moscow and had been initiated by Lenin himself.
So this is what Wikipedia says. I've not managed to find anything conclusive about Lenin's involvement (or possible lack thereof) so I'm here to ask what History says.
Did he order the execution or not?