It was stated by Miguel that he was binded to the Dead Sea by FATE to make sure Serge would not get to it. FATE is very powerful.
The reason why the Dragoons, The Devas, Lynx, Harle etc. are Frozen is because anyone who is not the arbiter of the FROZEN Flame shall freeze if they come near it.
Lynx cannot go in and out. He can go to the Dead Sea but he can't get near the flame either. Lynx is Wazuki turned into the body of a Panthar, with FATE controlling him and using him like as if it was a Biological being of FATE
The Dead Sea was destroyed because it was like if Miguel was beat, then the Dead Sea would automatically be destroyed.
Game evidance does not suggest that Lynx had anything to do with it. Simply FATE used the dimensional Distortion points and sucked the Dead Sea into the DBT.
What are you talking about the 3 Fate islands? Cloto, Atropos and the other are only the DATA banks. When you get close to them, they flew away. They contain all the infromation of the past, present and future.
In Home World, there is No FATE, as there is no Chronopolis. Instead, all the information up to 1010 or whenever the dimensional split occured is in the Save points (you know, the triangle fate thingies). It was stated that FATE could manipulate people in Home and Another through these, telling people what they should do unconsiously.
And as for Lucca, it did not matter what Dimension she was in,Lynx would probably try and get her into Another anyhow. I just think that in Home world, she is still alive. The only reason why Kid became a Radical Dreamer was in Another World to get revenge on Lynx and get to the Frozen Flame.