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Injection Fairy Lily [j. Injection Angel Lily]
This card's effect can only be used once per Damage Step. In other words, you can't pay 6000 Life Points to increase its attack strength to 9400.
The increase only lasts as long as the Damage Step (i.e. it's not permanent).
Remember that Lily's effect is used during the Damage Step. Cards that don't directly modify attack and/or defense strengths can't be used during the Damage Step. This means that [Mirror Force] and [Magic Cylinder] can't be against Lily AFTER she uses her effect. You would have to use either of those cards during the Battle Step, when your opponent states that she is attacking.