Engine for Lilithmon
Overview

[BT3-091] Lilithmon is a purple digimon that was introduced in BT3 Union Impact, is used to retrieve the option card from trash back to hand. The most disadvantage of this card is its condition for "when evolving" effect that you must have 10 or more cards in trash in order to return 2 purple option cards from trash to hand. So if you are unlucky to draw Lilithmon early, your game may not follow your strategy.
Lilith is not widely used in BT3 meta, players normally add 1 or 2 copies in their deck if the deck strategy relies on option cards. But with the zero cost option card for purple from BT4, it forms the best combo for Lilith to get more memory for purple player turn.
Mechanism
Using Lilithmon to retrieve then play the purple zero cost option card Jack Raid to gain total 3 memories

Jack Raid main effect is to gain 1 memory for every 10 cards in your trash (meant you get 2 memories if you have 20 cards in your trash). Player will tend to play the combo Jack Raid and Lilithmon in the late time of the game when they have enough card in trash: Evolving from a purple LV5 to LV6 Lilithmon with 3 cost and return 2 option card from trash to hand, then play Jack Raid to gain 1 memories, trigger Lilithmon "your turn" effect, get +2 memories when you play an option card. So total we have 3 memories for this play.


Lilithmon becomes more valuable when using her with the Omnimon Zwart from BT5 Battle of Omega. This combo is called Lilith Loop.
Here is brief summary of how to use this combo (assume we have more than 10 cards in trash).
Step 1: Evolve a LV5 to LV6 Lilithmon, retrieve 2 purple option cards from trash to hand by using Lilith's "when evolving" effect.
Step 2: Play zero cost option card Jack Raid to gain 1 memories, trigger Lilithmon's second effect, "your turn" effect: get +2 memories.
Step 3: Play the Mega Digimon Fusion, evolve this Lilithmon to Omnimon Zwart for zero cost, trash top 3 cards then play 2 purple digimon cards from trash that cost of 8 or less (LV5 Kimeramon is a good example).
Step 4: Using this Omnimon to declare attack to opponent's security or digimon, return the Lilithmon in its digivolution source back to hand to destroy 1 opponent's unsuspended digimon that has play cost of 12 or less (12 cost is equal to a LV6 digimon)
Step 5: Evolve the LV5 Kimeramon (or any LV5 from step 3) to LV6 Lilithmon that we just return back to hand in step 4, retrieve the Jack Raid option card from trash (in step 2) and one another option card, repeat step 2 to get +3 memories.
From now on if we have another Omnimon Zwart and white option card Mega Digimon Fusion in hand, we can repeat step 3 and step 4. By the way, Lilithmon can only use to retrieve purple option card, not white option card.
To get the detail deck review and deck reference, refer to the "Deck Review: Lilith Loop" post.