SORRY, no probably won't work.
If installed, "tasksel" should probably work. Let me fire up the atom. SORRY, tasksel only installs complete desktops in it's default ncurses mode and probably only ones obtained via Debian repos.
However - via "man tasksel" It appears that you can go totally cli and (as root)
which will show what tasks - desktop environments it has in it's database.
Unfortunately it is probably missing lxqt - for me I have lxde-desktop mate-desktop, xfce..., kde..., etc. but no lxqt-desktop, mine was installed quite a bit ago when lxqt was not in Debian repositories.
It would not hurt to try irc on freenode #lxde That is the irc that does support for LXQT. OFTC #lxde is the irc that supports LXDE.
How did you install Trinity? I hope others can come up with a better solution.