Lucifer's gamer name is MFNDevil. Eve is FirstWoman.
The back of Lucifer's sleeveless hoodie bears a subtle graphic of angel wings.
Lucifer finally hangs a lampshade on the elevator. "Lampshade hanging" is when attention is drawn to something within a plot that is implausible enough to almost break an audience's willing suspension of disbelief, and is sometimes done to acknowledge the writers are also aware of the oddness of the situation, and/or to add humor to a scene before then moving on to the substance of the story (here it's both). E.g., Lux is said to have top-notch security, yet throughout the series, surprise visitors - friends, family, strangers, and even dangerous enemies - are regularly able to access Lucifer's penthouse through the elevator.
Inside joke: during the awkward crime scene conversation between Dan, Ella, and an oblivious Chloe, the design on Ella's T-shirt has the phrase "This is Unbearable" and a picture of a bear covering its face as if in embarrassment.