What cat does Barney refer to during your first meeting with Kleiner in Half life 2?
The cat did not appear in any of these games:
- Half Life (Source)
- Blue Shift
- Opposing Force
- Decay
- Either of the Portals
- Half Life 2 or anything released thereafter.
I'm going to call this a noodle incident (TV Tropes link, you have been warned).
You all have missed the answer completely. It is simply a reference to a scene in the movie "the fly". The lab is even designed to be similar to the movie.