I believe these issues should be kept as separate as possible but regarding the LL's effort OP writes:

Now, it has been divulged to me that while she's not super into it, she does submit to him and even initiates maybe once out of every four or five times. She says she acts enthusiastic about it instead of lying there, and she has been keeping on a routine or schedule of sorts to make sure it doesn't fall to the wayside or be forgotten.

My reading is that the HL is unaware that this is what is going on under the surface of the changes he sees but at the very least its effects will bubble up and by inference the truth will become clear to him as time goes on. That will surely weigh on him and threaten to sink the entire relationship.

The reason for separating these things (massages and sex, indeed possibly everything and sex, will have to consider this line of thought) is that these other things we do for one another can, sometimes must, be unidirectional/selfless. There is a strong disparity (like 20:1) in massages in my relationship and that is fine. I give them in different places and times and on different parts as needed because I want to help her feel better. I'm not a professional though and she sees one for systemic issues, as OP's friend should do. Similarly though not perfectly congruous, she fills our lives with more visual beauty than I ever could hope and I am far and away the recipient here. I don't imagine that she laments (well, not much) my minor involvement in this enterprise.

But if I may project, I believe sex is at its best both a selfless and selfish act. OP's friend is bringing the former to the table and that is to be commended for a time as a first step, but ultimately it and other avenues of personal growth and barrier removal must lead to the latter. Because just as she is likely (but maybe not?) getting something emotionally satisfying out of his desire for her, so he must get the same satisfaction knowing and loving that she selfishly desires him. I conceive of it as two GGG lovers taking from and giving to one another in a kind of crescendoing upward spiral. If she can't find within herself a desire, direct and base (i.e. emphatically not some kind of quid pro quo), for sex with her SO then it will erode what he is getting out of it and instead spiral downward.