yeah, swapping to a 1.8L is a waste in effort...but going from a 1.9L to a 2.0 DOHC is worth a shot. I´m pretty sure that´s what Chad did quite well too.
Anyhow, turbo. A turbo is just a fancy aircompressor, its not car specific. However, understanding how your motor will react under boost is a weekend seminar in itself.
Im pretty sure an old 83-84 Escort Turbo, or EXP turbo manifold will bolt up to the 1.9L. I´m not sure what you´ll have to ditch in terms of AC or PS or anything like that in the LX but I´m confident it could be done. I had a roommate that ran .54BAR in his 99 Civic EX with the D16Y8 motor. Honda motors dont have the strongest internals, so I dont see why the LX could run like 6-8psi.