Don't know about lying on the refugee app, but posting pro-terrorism material would come under free speech unless you can prove it is incitement.
Arrested and imprisoned, so there must have been proof he was planning to, conspiring to, or actually breaking some law, presumably planning to go overseas and kill people would be against the law.
It certainly is a case of proving he is a terrorist (not a wannabe terrorist, can't see anything illegal about that, unless by wannabe you mean actively planning a terrorist act). Are we going to lock people up just for what they think? Or maybe we lock them up because of, you know, the vibe of what they claim to believe.
We restrict our freedoms we play into their hands, they don't spread terror for the fun of it, they do this to make our societies' cower in the face of their actions.
DS