Yes, Satan is devoting himself to a lost cause, for at the end of time God, not Satan, will win the struggle between good and evil. The Bible says concerning those last days that "the devil, who deceived them, was thrown into the lake of burning sulfur ... (and) tormented day and night for ever and ever" (Revelation 20:10).
I sometimes wonder if perhaps Satan actually believes his own lies, and has convinced himself that he will win. After all, his followers can be like that. The Bible says, "Evil men and impostors will go from bad to worse, deceiving and being deceived" (2 Timothy 3:13). Perhaps Satan is the same way both deceiving others, and being deceived himself.
But don't lose sight of what we do know for certain: Satan is absolutely opposed to God and His plans for the world. And that is why Satan works tirelessly to turn people away from God and draw them into his evil realm. He will use every device he can to deceive people and destroy their lives.
Don't let Satan deceive you or tempt you into thinking it doesn't matter how you live. Instead, make sure of your commitment to Christ, and draw near to God every day. The Bible says, "Be self-controlled and alert. Your enemy the devil prowls around like a roaring lion looking for someone to devour. Resist him" (1 Peter 5:8-9).