from the FAQ at zenithservice.com:
Home > Product Support > FAQ
Question PIP doesn't work properly
Product LCD TV
The PIP on our LCD TVs doesn't work the same as older analog TVs, so it causes some confusion. Most of our LCD TVs are setup under the assumption that HDTV or PC will be the main source. So, Component and VGA (RGB-PC) are the main sources. Therefore, you can only use TV (coax), Video 1, Video 2, or S-Video as the PIP source when using Component or PC as the main.
Main Picture Source Available Sub-Picture Sources
VGA (RGB-PC) or Component (YPbPr) TV (Coax), Video 1, Video 2, or S-Video
TV (Coax), Video 1, Video 2, or S-Video VGA (RGB-PC) or Component (YPbPr)
So you may be able to use it simultaneously as a computer monitor and a tv.
I looked and could not find your model listed in the Owner's Manuals section. No returns for a 22LCD3. I also didn't see any 22" models while looking for the manual. May be too new for the website or Zenith/LG just don't want it available electronically.