The goats do go to the lake of fire upon the inauguation of the millennium. Remember that the goats are those who are ALIVE at the beginning of the millennium. The GWT deals with those who are DEAD and resurrected for judgment after the millennium. The sheep are mortals who populate the millennium but they also die during the millennium. That is why Rev 20:5 refers to the "rest of the dead did not live again" until after the 1,000 years were finished.
Teaching regarding the resurrections are all over the place. There are two resurrections. The first resurrection of the dead occurs at Jesus' second coming. I believe the "rapture" and the second coming are a single event occurring at the end of the tribulation (Rev 16:15-16). We know that the dead in Christ are risen first, followed by the saints who are alive at His coming. However, what is not commonly taught is that all the unsaved dead are also resurrected at this time - not just the dead saints in Christ. How do we know this?
Jn 5:28-29 Jesus himself stated:
28 Do not marvel at this, for an hour is coming in which all those in the tombs will hear His voice,
29and will come forth—those having
done good to
the resurrection of life,
and those having
done evil to
the resurrection of judgment.
Jesus cites a specific hour (singular) in which ALL those in the tombs will be resurrected - both the "good" AND the "evil."
The Apostle Paul confirms the same thing when he stated: "and I have the same hope in God as these men themselves have, that
there will be a resurrection of both the righteous and the wicked" (Acts 24:15). Paul referred to a [singular] resurrection of both the righteous and the wicked which parallels Jesus' statement.
On the other hand, the second resurrection takes place at the GWT judgment where the dead are judged. The rest of the dead are those who lived during the millennium and are resurrected and judged according to "what they had done" (their works during the millennium). It is commonly taught that all the unsaved wicked from all ages of time are judged at the GWT. I don't think that is the case as both Jesus and Paul taught that there is one resurrection of both the righteous and the wicked at Jesus' coming.
Hope this makes sense as it can be confusing.