I think she's in the map where the message comes up saying "You can't catch me!" But I think she's either in the pond or in the top of the map where the ridge is.
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Anduril
Flame of the West
If you have not gotten the awareness skill, you may not catch her. Once you get it from Mesera in North Gidolian you may "catch her by hitting her until she "faints"
You need to have the Catch Dark Fairy mission. Then Heldan will give you his anti mindhunter hat. She will be flying around randomly in that map.
Good Luck
Hope that answers your question.
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Caution:
LabRat may go off at any time so please wear your helmet.