Lucien knows Amelia is a fantastic swordswoman, so he summoned his katana, to show her that he has a soul weapon just like she does.
But why did he stabbed the katana in the ground? Because he wants to show her that he is limiting himself, but still confident enough to beat her without a weapon.
He knows that Amelia is very powerful, but he wouldn't be able to fight her with a weapon while holding back enough to not harm her. He doesn't want to take any chances of hurting her.
Still, Lucien had hopes of winning, or rather, confidence in his speed. Because it increased even more after he reached the Mortal Realm and absorbed Aylin's Naginata into his soul.
Of course, the difference between Lucien, who is in the first layer of the Mortal Realm, and Amelia, who is in the seventh layer, is still quite significant.
Lucien kissed Lust while she mentally asked him. 'Are you going to use that?'
He replied. 'Yes. I need to show her that my methods are the most effective.'