I am pretty sure that either the TeXbook or Lesile Lamport's LaTeX users guide says \not is a slash with width 0 (and rather obviously ink outside it's official boundary). Whether that is the cleanest way to implement it in LyX is not a question I am qualified to comment on. -- Duncan (-: "software industry, the: unique industry where selling substandard goods is legal and you can charge extra for fixing the problems."
- \not Andre Poenitz