But how do they get there after they are judged and found to not be included in the Book of Life?
You are confusing Gehenna (lake of fire) with "hades". You aren't alone, ever since Catholics skewed eschatology Prots and everyone else continue in the same error.
Christ warned about Gehenna, not Hades, unfortunate most versions also confuse them, translating both as "hell". Young's Literal does not:
YLT Matt. 5:22 but I -- I say to you, that every one who is angry at his brother without cause, shall be in danger of the judgment, and whoever may say to his brother, Empty fellow! shall be in danger of the sanhedrim, and whoever may say, Rebel! shall be in danger of the gehenna of the fire.
YLT Matt. 5:29 'But, if thy right eye doth cause thee to stumble, pluck it out and cast from thee, for it is good to thee that one of thy members may perish, and not thy whole body be cast to gehenna.
YLT Matt. 5:30 'And, if thy right hand doth cause thee to stumble, cut it off, and cast from thee, for it is good to thee that one of thy members may perish, and not thy whole body be cast to gehenna.
YLT Matt. 10:28 'And be not afraid of those killing the body, and are not able to kill the soul, but fear rather Him who is able both soul and body to destroy in gehenna.
YLT Matt. 18:9 'And if thine eye doth cause thee to stumble, pluck it out and cast from thee; it is good for thee one-eyed to enter into the life, rather than having two eyes to be cast to the gehenna of the fire.
YLT Matt. 23:15 'Woe to you, Scribes and Pharisees, hypocrites! because ye go round the sea and the dry land to make one proselyte, and whenever it may happen -- ye make him a son of gehenna twofold more than yourselves.
YLT Matt. 23:33 'Serpents! brood of vipers! how may ye escape from the judgment of the gehenna?
YLT Mk. 9:43 'And if thy hand may cause thee to stumble, cut it off; it is better for thee maimed to enter into the life, than having the two hands, to go away to the gehenna, to the fire -- the unquenchable --
YLT Mk. 9:45 'And if thy foot may cause thee to stumble, cut it off; it is better for thee to enter into the life lame, than having the two feet to be cast to the gehenna, to the fire -- the unquenchable --
YLT Mk. 9:47 And if thine eye may cause thee to stumble, cast it out; it is better for thee one-eyed to enter into the reign of God, than having two eyes, to be cast to the gehenna of the fire --
YLT Lk. 12:5 but I will show to you, whom ye may fear; Fear him who, after the killing, is having authority to cast to the gehenna; yes, I say to you, Fear ye Him.
Christ's "prophecy/parable" the Pharisees (Rich Man) would not repent even if dead Lazarus was resurrected as a witness to them, does not depict Hades as a place of eternal torment. Abraham calls him "child/son", and both he and the redeemed with him wanted to comfort the Rich Man but could not. Like everyone else in Hades, he will rise on judgment day. Hades is NOT the place of eternal torment.
It is where the unsaved dead go to hear the gospel preached (perhaps for the first time), and make their decision.
Its also where willfully sinning Christians are liberated from slavery to sin they couldn't defeat in life.
The wicked go to the lowest sheol/hell, where they wait for judgment day and to be cast into the lake of fire/gehenna.
Gehenna is a place of PHYSICAL torment, wicked souls imprisoned in abominable corpses that will burn in eternal fire, and their worms will not die out. They misused the body God gave for evil pleasure, therefore the body now communicates the wrath of an offended God to the soul trapped within.
NKJ Isaiah 66:24 "And they shall go forth and look Upon the corpses of the men Who have transgressed against Me. For their worm does not die, And their fire is not quenched. They shall be an abhorrence to all flesh." (Isa. 66:24 NKJ)
But not all suffer in gehenna eternally. Some only for an instant and then they are annihilated, "burned up":
You shall trample the wicked, For they shall be ashes under the soles of your feet On the day that I do this," Says the LORD of hosts. (Mal. 4:3 NKJ)
So Christ warned about fearing Gehenna, not Hades:
YLT Matthew 10:28 'And be not afraid of those killing the body, and are not able to kill the soul, but fear rather Him who is able both soul and body to destroy in gehenna. (Matt. 10:28 YLT)