Was the lunar module also used to perform a barbecue roll?
Yes, although it took them a while to get there, according to the Apollo Flight Journal.
Starting at about 7 and a half hours after the accident, the crew began rotating the spacecraft periodically 90 degrees at a time to approximate the effect of the passive thermal control roll:
063:24:52 Lousma: Okay, Aquarius. We're going to dispense with this control mode. We'd like you to fly the machine back to the original attitude that you had, and we'll go PGNS Attitude Hold, and then we've got to get that ball off the line to save some power. And then, in order to keep even heating, every 15 or 30 minutes, we'll give you a call to give us 90 or 180 degrees of roll - of yaw.
(Because of the way the spacecraft axes are defined, yaw for the LM is roll for the CSM.)
I believe they did this manual PTC procedure because the attitude indicators were going to be shut down, so the orientation of the spacecraft would be difficult to monitor.
The manual PTCs continued for at least another 10 hours; at 79:27 in the flight came the big "PC+2" burn on the LM's descent engine to speed up the return to Earth, and after that they established a relatively normal PTC roll. One of the big challenges after the accident was trying to maneuver the massive CSM/LM stack using only the thrusters on the lighter LM end of the spacecraft; Lovell kept finding that trying to roll the stack induced unwanted pitching movement, so getting into a stable roll was a challenge, but eventually they achieved something satisfactory:
082:14:43 Lovell: Okay. Now are we sure that this PTC mode is good enough so we don't [garble] get crossed up later and get out of configuration.
082:14:53 Lousma: Stand by 1 on that, Jim. Okay, Jim, as far as we can tell right now, the PTC looks as good as any PTC we've ever seen in a CSM, so we're going to go with what we've got.
The PTC did tend to go into a wobble over the remaining days of the mission. They stopped it and re-established a stable PTC at around 101 hours, although by that time Lovell seems to have been getting a little irritable:
101:40:05 Lovell: And I'm copying down the reestablishing ... PTC maneuver that Charlie gave me. Step 5 was, "When rates are less than 0.05 degrees per second, Attitude Control Yaw to Pulse." And just how am I to get my rates down to 0.05 degrees per second. My ... My rate indicator, at the best, is 0.1 of a degree.
101:41:44 Brand: Jim, this has been tried in the simulator by Charlie and others, and what they recommend is that you null your rates on the error needles until you see no movement whatsoever, and then wait another couple of minutes, and that should do it. That's the only way we can tell. Over.
101:42:09 Lovell: Okay. I'll give it the old college try.
101:42:12 Brand: Okay. And if you can't attain that, why, of course, just the best you can do. We'll have to give it a try. Maybe it won't be quite like the simulator.
101:42:24 Lovell: Right.
PTC was stopped again at about 105 hours to accommodate a midcourse correction maneuver, and reestablished immediately thereafter. This one was wobbly, and shortly after another re-establishment, a helium pressure vent disc burst, which actually reversed the direction of the barbecue roll!
The next day, the LM cabin was growing so cold due to the power-down measures that PTC was given up:
133:22:08 Lousma: Okay, Skipper. We figured out a way for you to keep warm. We decided to start powering you up now, and what we want you to do - what we want you to do is take your entry LM Prep checklist and start at the top where it says "Bat 5 Normal FEED on," and then jump over as it says to your 30-minute activation, and do all of the 30-minute activation up to, but not including, the burn. You copy?
133:22:52 Lovell: Okay. If I understand you correctly, then that gives me leeway to maneuver when we get up to activation complete, and we can be in position for the burn, but we will not burn. We don't have a PAD anyway. [Long pause.]
133:23:15 Lousma: That's affirm, Jim. You could maneuver to burn attitude, or you could maneuver to an attitude which should put the Sun in the windows to warm the place up.