(No sources; this is my own thinking.)
We learn that we must take positive action to affirm our relationship with God and k'lal Yisrael. Yisraelites who merited being spared from this affliction were nonetheless affected if they did not take action.
We learn that we sometimes must take public action to affirm our status as Yisraelim. The blood was placed on the doorposts and lintel, not on the inside of the door or on the floor just inside (where the destroyer would still see it in time). Publicly identifying ourselves as Jewish sometimes brings challenges, but if commanded by God to do something public we must nonetheless do so, whether we're talking about blood on doorposts in Egypt or covering one's head today (or refraining from work on Shabbat even if it causes loss, or keeping kosher even if it means subsisting on salad on business trips).
(I'm not sure what point you're raising about eternal torah versus specific-time commandments. We have other incidents where God commanded specific people to do specific things, ranging from journeys to military conquests to the akeidah. That doesn't necessarily mean there's a direct parallel today. But in the specific case of the last plague in Mitzrayim, which is what you asked about, I think there is.)