The flight plan makes clear that this is not the case.
> Perhaps a fuel transfer or some guidance calculations or some other maneuvers.
Even without reading the details of the flight plan, the LM was designed to carry just enough fuel to get down to the Moon's surface and back up again, with no extra fuel for other maneuvers; there wasn't any margin for any extra if the mission was to be doable at all. So it doesn't seem plausible that the CSM would have had to depend on getting some fuel transferred back from the LM in order to execute TEI.
As far as guidance calculations, that doesn't seem plausible either. The CSM, having been in a single stable orbit the whole time, would be expected to have much better guidance information than the LM, which had just executed a series of maneuvers, some of which were under manual control.
My point was just that if our only information is that the LM returned to the CSM and was jettisoned before TEI we can’t deduce that the LM was not needed for TEI.
But there is other information available:
https://lithub.com/what-if-we-got-stuck-on-the-moon/
Command module pilot Mike Collins, who could only keep orbiting in the mothership while his comrades waited out the countdown to lunar liftoff, worried enough for all three of them. “I have been flying for 17 years, by myself and with others,” he would write in his post-mission memoir. “But I have never sweated out a flight like I am sweating out the LEM [liftoff] now. My secret terror for the last six months has been leaving them on the moon and returning to Earth alone; now I am within minutes of finding out the truth of the matter. If they fail to rise from the surface, or if they crash back into it, I am not going to commit suicide; I am coming home, forthwith, but I will be a marked man for life, and I know it. Almost better not to have the option I enjoy.”
Two key sentence fragements: "leaving them on the moon and returning to Earth alone" and "If they fail to rise from the surface, or if they crash back into it, I am not going to commit suicide; I am coming home, forthwith". Both indicate that Collins fully believed he could execute TEI should the LM fail to return. The only way he could possibly "return[ing] to earth alone" should the LM "fail to rise from the surface" would be if the CSM could execute TEI without the LM ever returning from the lunar surface.
Which would indicate that the LM was not required in any way for TEI.
