If we believe that the various Satans (in the original Hebrew, literally "adversary," and rendered without the definite article so there are probably multiples of them) are in fact one and the same with the Devil (singular), this link-up doesn't even occur until the Book of Revelation which is firmly a new testament thing and wholly unsupported by any of the old testament or ancient Hebrew sources from which it's derived. Making all the assumptions required on basis that this is so, then whoever he was killed a lot of people in Revelation. But not until then.

In old Hebrew tradition, the Satans are sort of the prosecuting attorneys for god. They work for him in order to tempt the faith and righteousness of various people. Several mortal people are also given the moniker of "Satans" when they're working against the interests of god or various other individuals.

Meanwhile, the notion that Lucifer is also one and the same with the Devil or any kind of Satan is a much later interpolation made when the church(es) of the era wanted to insert a bogeyman into their religion and they needed a justification for it, some time in the AD 200s. Lucifer is identified as the king of Babylon, a mortal, when he has attracted god's ire in his sole appearance in Isaiah 14. The situation has become so warped that his name was finally removed in the New International Version of the bible and he's simply referred to as the "morning star, son of the dawn." (Isaiah 14:12, if you want to go have a look.)

Modern pontificates will also insist that the king of Tyre in Ezekiel 28 is also somehow the Devil, which is dubious. Even if he were, and god were speaking allegorically for precisely half of his rant as we are thus demanded to believe, god smokes him at the end of the passage anyway so it's a moot point.