As far as I noticed Tower of Joy triggers (surprise surprise) when Robert wins his Rebellion.
An playing as Ned I got to find out that the actual OUTCOME of the event is not displayed to the player, for some reason.
The event works fine, no matter the outcome (I reloaded several times to see what happens if Dayne slays all my men), but a pop-up like "Now the Kingsguard are all dead, I will safe her....but no, what is that?" or, different outcome "Due to my failure Robert will now have to live without her...not that this will matter to me anymore" would be really nice since right now, I was waiting for like three months for the event to continue, only to then see in the character pages Lyana was happily married to Robert (and again had a legitimate Targaryen bastard, but he didn't seem to mind that. Guess she judged him wrong in the books

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same goes for the other option, I win all duels, wait for months, nothing happens until I check my family tab to notice Lyana died and I, Ned now have a bastard (which the AI again named Joffrey. Oh cruel world)
So I'd guess in the end of line something is missing to trigger the correct messages (as mentioned, the effects take place as intended no matter what option the game chooses to happen), since with all the love put in the detail and quest-texts I highly doubt the mod-team did not bother to create one more popup telling Ned he finds his dead sister- after all Robert gets his popup just fine in the end of the event.
On a further sidenote, Theon Greyjoy 18 Martial? Like , really? I was already wondering about Catelyn being proud (where she actually should be humble) and Cersei being Gregarious (where she should be, well, Paranoid at least), but 18 Martial Skill for Theon breaks with the lore way too hard imo.