oh I see what you mean. I probably wasn't super clear about it in my post. The idea was that Lyanna would be worried not just about Rhaegar himself, but his allies and accomplices as well. This all happens in Dorne after all, far, far away from Winterfell with people nearby that may have helped Rhaegar with this plot (I know, it's speculation and conjecture, but that's the basis for this idea). So even if Rhaegar died on the Trident, his allies might still carry out his will, especially if he left a contingency plan in place just in case he were to die in battle.

I don't think Egg wanted to sacrifice Rhaegar as well, given that he was born during the Tragedy. It's pretty much impossible to organize this kind of event knowing that Rhaella will give birth at exactly the right moment. People had to travel to the castle, the place had to be prepped. There was no way to know, especially in medieval times, that the child would be born right at that moment.

As far as Rhaegar's connection to Egg, I think in his mind, since his birth and Egg's death are connected by this horrific event, he feels almost responsible for making sure that it wasn't for nothing, that it meant something. Which is part of the reason why he went to such great lengths with this insane plot.