Regarding a passive act that indicates mourning, The Tur (YD 400) writes that Rabbenu Tam would regularly get a particular aliya to the Torah. When he was a mourner, they didn't call him, but he went up anyway, since his absence would be considered "public" mourning which is generally forbidden on Shabbat. It seems from this, that even not engaging in Torah study can be considered public mourning. Thus, if one's absence will be noted, it seem likely that one should attend the shiur on Shabbat. Otherwise, it seems likely that one ought to refrain from showing up for the shiur (or even walk out if it wouldn't be noticed).
Additional views are cited in the Beit Yosef there. To summarise: according to R. Isaac of Dampierre, there is no prohibition of studying Torah on Shabbat, since Torah gladdens and one must be happy on Shabbat. According to Rabbenu Tam and Hagahot Maimoniyot, there is a general prohibition to study on Shabbat, but it is permissible in public. According to Rabbenu Tam, passively not learning is considered public mourning if it will be noticed, and thus, although Torah study is prohibited, if one's absence will be noted, he should study. According to the Hagahot Maimoniyot, however, it would be better to leave rather than engage in Torah study even if one's absence will be noted.
Thus, according to R. Isaac one should certainly attend the lecture, according to Rabbeu Tam, one should attend if his absence would be noticed, and according to the Hagahot Maimoniyot, one should not attend the lecture even if his absence will be noticed. The Beit Yosef notes that R. Isaac is a minority view whom halakha does not follow. Although he doesn't take a stand on the dispute between Rabbenu Tam and the HM, in the Shulhan Arukh he only mentions the view of RT, and neither he, nor Rema mention the HM's suggestion of having someone leave rather than participate in Torah study. Instead, the more popular view seems to be that if a lack of Torah activity will be perceived as mourning, then it should not be avoided.
Regarding the question of whether listening to a lecture would be the same as learning actively, it should be noted that according to many many Rishonim, including Yereim, Ritva, and Rambam (as understood by R. Rabinovitch), the mitsva of Torah study applies to non-verbal study. This is the opinion of numerous Aharonim such as the Yeshuot Yaakov, R. Yaakov Emden, R. Kook, and R. Soloveitchik, to just mention a few (see here).
Accordingly, it is not clear why there would be any distinction between looking at something yourself, reading it, or listening to someone else reading it.
Furthermore, even according to the apparently minority view who holds there is no mitsva in non-verbal study, it is not at all clear that that would have any bearing on the question at hand, as the prohibition is likely due to the fact that Torah gladdens a person, as is the reason for the prohibition on the 9th of Av (see Ta'anit 30a) in which case Torah study that doesn't happen to fulfill a mitsvah would likely be equally banned.
Regarding whether or not the prohibition relates to Torah gladdening a person, see Tosafot Moed Kattan (21a s.v. V'assur) which discusses the view of R. Isaac of Dampierre, regarding the opposite question; learning Torah that saddens a person. Originally he suggested that one should be strict, since unlike the prohibition on the 9th of Av, the prohibition of a mourner isn't explicitly stated to be due to happiness. However, later he ruled that is is based on happiness, and that one may learn depressing things. Tosafot notes that this is similarly the implication of the Yerushalmi.
Similarly, many Aharonim assume that the prohibition is due to joy. These include K'li Y'kar to Genesis (27:41), Kitsur Shulhan Arukh (210:1), and Yalkut Yosef (YD 22:6).
Accordingly, there would be even less reason to suspect that this would be any different from any other Torah study, and would presumably be forbidden.
Alternatively one could suggest what amounts to a new derasha. The prohibition for a mourner to study Torah is based on Ezekiel's instruction to be silent (Ezekiel 24:17), as stated by Rambam in Hilkhot Evel (5:15) based on Moed Kattan (15a). Accordingly, Torah study that is silent is permitted. In my opinion this line of reasoning is not compelling.
In light of the above, I see no reason why "passive" study would be any less forbidden. Indeed, R. Yitshak Yosef has a related discussion in Yalkut Yosef (YD 22:11). He writes that a mourner may not think Torah thoughts. He suggests that there might be room for leniency on Shabbat (as noted above, according to some there is no prohibition of Torah on Shabbat at all), but nevertheless writes that one should refrain from this.
Importantly, he writes (22:10) that one could be lenient to learn Torah on Yom Tov.
Edit: I now see that some of these points (but few of these sources) are mentioned in this post.