The simplest, and most likely answer is that Fox just needs the show to fit into it's schedule and this was the best way to do it.
Lucifer is not alone in this setup; I believe Gotham has a similar quirky scheduling thing going on. The problem basically boils down to having too many weeks in the TV season, and not enough episodes to fill them
Typically, a broadcast network first-run show has around 22 episodes. The fall TV season runs approximately Labor day (early September) to Memorial Day (late May), which is closer to 44 weeks. So there's not enough episodes of any series to run every week.
The networks solve this problem in a few ways, one of which is the "mid-season finale". This happens to most network shows during the winter holiday season (Thanksgiving/Christmas/New Years). That period tends to be full of specialty programming (parades, holiday specials, etc), re-runs, sporting events, etc. It also tends to have a dip in the viewership numbers as people are busy doing other things, taking vacations during their work holidays, etc. A nice side effect is to give the networks a month or so of extra time in the spring.
Lucifer did go on a winter break on Nov 28, which was not at all unusual. However, there is something a bit unusual about it's return. The second half of the Lucifer season is not coming back on the air until May, with 9 episodes that will run through the end of June. That's pretty late for a fall show (by that time the summer stuff is usually getting started). But that left three episodes they needed to air, and for some reason they chose to air a three episode "story arc" bridging the two halves of the season (the Chloe/Lucifer/actual relationship story), ending on a second cliffhanger.
While we can guess that Fox did this for scheduling reasons, exactly what it was about their schedule that they were trying to solve is likely a closely-guarded secret. It's possible they aren't planning to renew the show, so they're slowly letting it die off into the summer where the low ratings won't matter. It's also equally possible that they don't have another show to put in it's timeslot in June and they need it there more than they need it in the spring. It's possible this is just an experiment to see if they can drum up interest in a show by having multiple cliffhang endings (that's the "official party line" from Fox -- that this was a creative decision -- but they always say that.)
