Bestiary 2 pg. 38: "A chaotic good 7th-level spellcaster can gain a lyrakien as a familiar if she has the Improved Familiar feat." So while most improved familiars only require one step away, the monster entries for several improved familiars (including the lyrakien) specify that that creature is more strict about what masters they'll work for - that they'll only accept full alignment matches.
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