From what I have gathered, after the explosion, Houston debated the on the quickest and safest way to get them back to earth. The decision was the free earth trajectory. But they were not on that trajectory at the time, so yes, the first burn using the LEM was to get them on that trajectory. That got little mention in the movie. After getting around the moon, they performed another LEM burn to get them back sooner. That was mentioned in the movie briefly. Then at some point Houston realized they were too shallow and they would need to perform a corridor correction burn using the LEM. This one would have to be done with no guidance computer because they didn't have the electrical power to spare. That is the one that was highlighted in the movie. That little old LEM saved their bacon, and I ain't talking Kevin.
BTW I didn't know Kevin Bacon had passed away, did you?
This is Mercury control, over and out!