"Injection Fairy Lily" is one of the few cards in the game to activate specifically during Damage Calculation, meaning that aside from cards that negate the activation of effects, there is little that can be done to stop her effect from activating if her attack is successful.
Additionally, this means if "Lily's" attack is negated or otherwise interrupted, you won't have the opportunity to pay the cost for her effect.
"Injection Fairy Lily" works well with "Cybernetic Magician". By discarding a card, and paying 2000 Life Points, "Injection Fairy Lily" becomes a 5000 ATK Spellcaster - which is perfect for dealing large amounts of damage when you can directly attack your opponent's Life Points.
Equip "Injection Fairy Lily" with "Unstable Evolution" and attack to make her have 5400 ATK if you have less Life Points than your opponent and 4000 ATK if you have more. This is a powerful first attack because she is guaranteed to have 5400 ATK if you and your opponent both had the same Life Points when you attack.
This card can work well in a deck relying on "Black Garden" as you summon this card, it goes to 200 your opponent gets a Rose Token and you attack it then pay 2000 Life Points to deal 2400 to your opponent.
It's better if you summon "Injection Fairy Lily" before activating "Black Garden", so its attack is not halved.
Equip her with cards like "Mage Power" and "United We Stand" as these cards not only increase her ATK, but her DEF, as well use her effect once to deal massive damage then switch her to defense position and use her as a shield until the time is right and preserve your life points, or go on the offensive without using her effect until you have a clear shot at your opponent's life points.
"Infected Mail" allows you to attack directly, at the cost of sending her to the grave afterwards.
As she is already difficult to destroy by battle, using "Gagagashield" and/or "Spellbook of Wisdom" in conjunction with "Injection Fairy Lily" can protect her from destructive card effects making her even harder to overcome.
For added support, "Spellbook of Power" can also be used to not only increase Lily to a potential 4400 ATK, but also search out "Spellbook of Wisdom" if she destroys a monster.
Because of her low original attack, "Power Frame" is a good card to use in conjunction with Lily, especially if your life points are too low to use her effect. Alternatively, her effect will then allow her to become greater than the monster that triggered Power Frame, letting her kill it with her next attack.
Since you may not want to pay such a heavy cost to destroy a defense position monster, equipping "Lily" with "Fairy Meteor Crush" or using the effect of "Ebon Arrow" can allow you to continue to inflict damage to your opponent and balance out the cost paid for "Lily".