This might answer your question for the first part -------
this is your statement here from above -----
you said ---------but do you have any idea why satan held the power of death
I say
Satan was the means of introducing Death by Tempting Adam and Eve to Sin -but He didn't cause Spiritual Death he posed a Question to Eve and Eve herself took the bait -----so Satan by his Tempting humans to sin held the power of death to those who acted on Satan's promptings -------We don't sin because we have to ---we sin because we choose to ------
Scripture says the wages of SIN IS Spiritual Death----Satan is the tempter to get us to sin --so Satan holds the power to temp us into sinning --so he held the keys to death until Jesus came and died and was resurrected and then Jesus got the keys back from Death to Life --If we accept Him -----if we don't accept Jesus we are sinners not Saints and ---the wages of sin is spiritual death -----
-------So for unbelievers there are 2 Deaths -------
That is how I see that ------
I say ----
as far as your question on Satan being thrown into the lake of fire goes -------
this says why -------don' know if that helps you --------
Topical Bible Verses
Topicalbible.org
Revelation 20:10
And
the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.