This is pretty nifty. I've managed to get a lewd ending through maxing out lust, Mating Press, and Tickle. Though that last one was very tricky and required stacking the deck with Thundershocks and Lost Grimoires!
Couple of glitches I've noticed. If you play with a lewd deck in the game shop and win by maxing out the lust bar orgasming Kate appears at the end, but stays on screen even after the duel! And related to that, you can have three decks, but despite selecting deck two I still duelled with deck one (I hadn't intended to face Healing Girl with my lewd deck!)
I got warning that my deck contained illegal cards (and also that I had more than four Thundershocks and Life Orbs), but it still let me play.
I'd love to see some consequences for losing, or for Kate to be able to play some lewd cards in return, but from your other comments that doesn't sound like it would be possible with how the AI works :(