Lucifer in the show, on the mortal plane, does not have his full range of powers. In the pilot episode, Pilot, Delilah is shot in front of Lucifer, and he couldn't stop that. Later, Decker and Lucifer are shot at, and while Lucifer was unaffected, he couldn't stop Decker from being shot. He has to save her, the normal human way, by getting her to a hospital.
In A Priest Walks into a Bar, Doyle shoots Conner, but Father Frank, in a spur of the moment, heroic, frankly godly manner, jumps in front of a bullet before anyone can react. Lucifer had no chance to stop it.
Remember, Lucifer has lost much of his power. He's lost his wings as well. He needed Amenadiel to try to get them back. At which point, Amenadiel, who is a fully powered Angel (supposedly) working on God's behalf, uses his powers to help. He slows down time for the humans, but not Lucifer, allowing Lucifer to walk around like normal. And when they fight because Lucifer burns the wings instead of letting Amenadiel take it, Amenadiel beats him easily. Of course, in this episode, Amenadiel resurrects the dirty cop Malcolm, with his powers.
In short, Lucifer can't save anyone better than a normal human could. He's barely more powerful than the average person really. He doesn't have a full range of angelic powers.
Considering the ending to the episode where:
Amenadiel tells Malcolm he wants him to kill Lucifer. With a seemingly normal gun. Suggesting that Lucifer is on some levels mortal.