Based on the long scene for the rescue of Lindsey and the fact that the movie continues even after the mission was a failure, Ethan could have just gone back home. The first plot that we are aware of has come to its end. Instead Ethan takes it upon himself to make this personal. The rescue is now more than a device to keep the show going.
Ethan must be a senior agent by now, so he must know of other deaths that happened in the agency. Also Lindsey was the only person he recommended for field duty. At the end, Ethan gives his wife a short intro to shooting a gun, which could be seen as how he trained Lindsey for field duty.
Does this indicate that the relationship was more than platonic?