Wait....
Let me get this straight....
a) you wanted to port Ubuntu (or something like that) to the PSP
b) you wanted to make a HB channel app
c) I believe I read more announcements in the past from you of glorious things you wanna do....
And now you're asking how to compile stuff for having it running on the PSP???
Are you serious? (have you ever been?)
Do you have ANY experience in coding? Especially on the PSP or another gaming platform for that matter?
Well, to answer your question:
LUA is a scripting thing, d/l it, read the docs and it tells you where to put what to run your scripts.
(Can't help more on this, as I've never used it.)
For C/C++ app:
Get the PSPSDK / toolchain from PS2DEV, install, make code, type "make", done....