I thought I'd offer a line of response but it's based on the argument summarized in the 2015 post. Please take this with a grain of salt. I haven't seen the text of the most recent lecture, so I'll respond to the argument as offered.
The Main Argument
P1. Homosexuality is a preventable disability.
P2. Disabilities ought to be prevented and cured (when they are preventable).
C. Homosexuality ought to be prevented and cured.
The Ancillary Argument for (P1) is contained in this passage:
"The first things to recognise is that homosexuality is a disability. For a homosexual is unable to enter into a loving relationship in which the love is as such procreative."
I think it's a terrible argument. First, a general comment. The passages suggest that the moral duty is somehow grounded in considerations having to do with the people who (allegedly) suffer from this disability. I think this is strange for a number of reasons. First, it seems to deviate from the more familiar natural law arguments where the duty seems to be grounded in something like the duty to maintain the traits of our person that enable us to discharge our duty to enter into an appropriate relationship to some sort of god. I don't see any trace of this sort of argument here, so I wonder if the proponents of natural law theory would agree that this turn to considerations that appear to have to do with a more narrow understanding of well-being is just wrongheaded.
Alright, so let's turn to the argument. I don't see how the ancillary considerations offered in support of (P1) could possibly carry the weight. They'd have to show that, somehow, it's not just good to 'fix' something, but that we're duty bound to do so at some expense. The expense, of course, is paid largely by the people we're supposed to fix. I wonder what background picture of well being and the duty of beneficence could support this line of thinking. If we're assuming some combination of subjectivism about well-being (e.g., a view on which a person's life goes better for them if desires are satisfied or they experience certain pleasures), the whole thing appears to be a non-starter because it's hard to see how we'd maximize the relevant agent's well-being by forcing them to try to correct their homosexuality. If we're assuming something different, something like an objective list theory, I guess I'd say that I'd want to see some sort of defense of the assumption that the relevant goods belong on an objective list. Thinkers like Aquinas never thought that procreation would belong on that list since he didn't think there was any p.f. duty to procreate (you didn't need to defend the choice to be celibate, for example, nor did you need to defend marrying someone known to be incapable of having children). Even if there was some defense of the objective list view that included something about procreation on it, there's the further challenge of explaining why the realization of that good isn't just good but something that generates a duty to engage in actions that make people miserable and generate the kinds of social stigmas that homosexuals have had to suffer under for a very, very long time. Even if I granted (which we shouldn't) that a life is, ceteris paribus, better if it contains a relationship in which love is coupled with natural procreation, I don't see any reason to think that there is some general duty to get people to realize that good (with the application of social pressure, self-denial, therapy, etc. that's known to cause great amounts of misery). It would be outrageous to do this by meddling with people's choices between a life of abstinence and a life in which someone indulges in sex, a choice between available partners in which some but not all are capable of having children naturally, and outrageous to do so in this case if there wasn't anything special about this case.
That raises the question: is there anything special about the case of homosexuals? I don't think so. Swinburne does. I think it's cowardice for him not to come out and say what it is. (Or maybe he's just getting really sloppy and didn't notice that there are morally licit choices that result in a life in which you don't enter into a sexual relationship that has the potential to yield children.)
There are also problems with the assumptions about conversion, the oddity of thinking that we have duties to 'fix' disabilities generally, etc., but we don't need to get into that. It's pretty clear that this is a bad argument for just the reasons outlined above. My worry is that Swinburne doesn't see how bad it is. How could he not? I suspect that there's something that prevents him from seeing what's obvious. I don't know if it's ugly or sad or whatever, but someone should fix him and his shoddy thinking. It's preventing him from entering into loving relationships with talented people because he can't help but see them as less than fully human. It's fucking tragic.