Lucifer's badge number is "666" with a Lieutenant Detective rank (above Chloe). Going from the blue enameling in the letters and numbers and the slight design differences from Chloe's badge, he seems to have liberated it from the "¡Diablo!" props department.
When Mazikeen attempts to recreate her fight with Amenadiel from Manly Whatnots (2016), she is wearing the same clothes, earrings, and hairstyle as she did then, and attempts to get him to don his original robes. The instrumentation and beats of the song playing over the fight are even similar to the music that played over the earlier brawl. In the earlier episode Amenadiel's goal was to get Lucifer to go back to the way he used to be. Here, Mazikeen is trying to get Amenadiel and herself to return to the way they used to be.
Tagalog is a dialect in the Philippines and is the main basis of the national language (Filipino). The lines that are not garbled can be roughly translated into the below (those in straight brackets are filled in based on what Lucifer summarized to Chloe right after)
Lucifer to Danilo: Nagsasalita ba siya (Jovita, Danilo's grandmother) ng Tagalog? (Does she speak Tagalog?" Danilo: Oo, nagsasalita siya ng Tagalog. (Yes, she speaks Tagalog). Lucifer to Jovita: Kumusta ka, madam? (How are you, madam?) Jovita: Mabuti. kayo ba'ng mga pulis? ...Ang naaalala ko lang, [iyung medyo matandang lalake pumasok] dito sa tindahan ko, bumili ng mga bulaklak na lilies, [tapos nag-Uber paalis.] (Good. Are you the police?...I only remember [this middle-aged man came] into my shop, bought these lilies, [then rode away in an Uber.])
Lucifer to Danilo: Nagsasalita ba siya (Jovita, Danilo's grandmother) ng Tagalog? (Does she speak Tagalog?" Danilo: Oo, nagsasalita siya ng Tagalog. (Yes, she speaks Tagalog). Lucifer to Jovita: Kumusta ka, madam? (How are you, madam?) Jovita: Mabuti. kayo ba'ng mga pulis? ...Ang naaalala ko lang, [iyung medyo matandang lalake pumasok] dito sa tindahan ko, bumili ng mga bulaklak na lilies, [tapos nag-Uber paalis.] (Good. Are you the police?...I only remember [this middle-aged man came] into my shop, bought these lilies, [then rode away in an Uber.])
Serial killers are often found to have a history of torturing and killing small creatures before turning to human victims. The killer's apartment has a wall of different missing pet posters and is ominously filled with obviously formerly occupied wire cages and small taxidermied animals and insects.
Klumpsky's apartment number is 507, which is also the season and episode number of the episode.