For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
As far as I am aware, he will not. I'm not sure if he can, however the Bible clearly says that Satan will do all he can against truth during the end-times.
Is it possible for Satan to repent and for God to forgive his actions?
I guess it all depends on HOW "you" view the purpose for the Lake of Fire
And the devil who deceived them was cast into the lake of fire and brimstone, where [are] both the beast and the false prophet; and they shall be *tormented day and night for the ages of ages.
He's "tormented" in this location "day and night" for the ages of ages - will he repent AFTER these ages? It's up to God.
Interesting enough, there's "brimstone" in this "fire". Same properties as Sulfur; My Strong's dictionary for the Greek of this word has this under it:
g2303. θειον theion...sulphur "...burning brimstone was regarded as having power TO PURIFY"....
then the Greek for "Torment."
g0928. βασανιζω basanizo...to torture
The primary meaning is to "torture". Yet, under the definition is this interesting "2 cents" as to HOW and WHY the word signifies torture
"to test (metals) by the touchstone, which is a black siliceous stone used to TEST THE PURITY of gold or silver by the colour of the streak produced on it BY RUBBING it with either metal" ---> by which "rubbing these metals" is the "painful" portion...but obviously has a purpose
Will Satan repent from his actions in this all consuming fire and brimstone while being tormented and tested for his purity? Each it's own to the answer
I am not God. However I know that NOTHING is impossible for God. God can and will do whatever He wants.