lxterminal forks off a child process. Think about it. That child process is the interactive shell that is attached to the emulated terminal by
lxterminal (or whatever alternative program one has supplied with the
-e option). It in turn makes further grandchild processes, depending from what one has actually done in that shell.
lxterminal closes the master side of the pseudo-terminal that it uses, which looks like a terminal hangup as far as the slave side is concerned. The slave side is what the interactive shell sees as its controlling terminal. So the shell should be seeing a normal terminal hangup, generating a
SIGHUP to the session leader if the terminal's
-hupcl setting is on. That session leader is that shell process.
The session leader is responsible for job control within the session, and for passing the hangup signal along to all of its jobs. Obviously, if you have
disowned something run by that shell, or
nohupped it, the session leader does not pass along the hangup signal and that something will continue to run even though
lxterminal has been terminated and the master side of the pseudo-terminal has been closed. That's what
You need to sort out why whatever it is you are running in that interactive session is not dying when the pseudo-terminal is hung up. You haven't told us anything about what that is, and we aren't telepathic. So there's little to suggest beyond generalities about what session leader shells are designed to do.