The Lovers Arcana DID choose him and not Lizel. If she had snuck in and left it by his pillow the Arcana wouldn't be talking to him or respond to his requests so quickly. Remember how everyone who finds out he can hear the Arcana talking to and doing things for him on it's own volition is shocked? That's because it's a sign the Arcana REALLY likes him. All the other Arcana holders don't hear their Arcana talking, requests for knowledge takes a while to complete, and the Arcana never does something on it's own volition whether big or small. That's why Lizel was really happy, and jealous, to hear that the Arcana was acting like an alarm clock to wake MC up in the morning without MC telling it to. While Lizel does seem to love MC it seems to be based on something that happened in the past when she was just another corrupt Devil noble following the party line of doing things for self interest and believe that only idiots find love and compassion worthwhile. Likely something happened with MC that got her to care about others again.