Hmmm, yes, there are some interesting possibilities. I do think that whatever we choose should highlight mortality in some way.
So far, our frame stories have been:
Season 1: (TA 2941-42) Ten-year old Estel, growing up in Rivendell, is taught the history of the world by Elrond. His mother Gilraen strives to make certain her son is raised as a Man, not an Elf. (The Hobbit happens this year.)
Season 2: (~TA 2943-5) Arwen, visiting her grandparents in Lothlórien, is saddened by a friend's decision to sail West. She ponders the place of Elves in Arda - Valinor or Endorë?
Season 3: (TA 2947) Teenage Estel rebelliously leaves Rivendell without permission and joins the Dúnedain, who are involved in fighting off an incursion of wolves during a harsh winter. Estel's rivalry with Halbarad's son costs Hamilcar his life, and Estel returns to Rivendell with the sons of Elrond.
Season 4: (TA 2948) Bilbo travels with Gandalf and Balin to revisit Dale and the Lonely Mountain for the 7 year commemoration of the Battle of Five Armies. Tensions between Dwarves and Elves threaten to mar the celebration, but resolution of an old grudge helps to heal some of the mistrust.
Season 5: (TA 2949-2950) ???
Season 6: (TA 2951) 20-year-old Estel learns that he is the heir of the chieftain of the Dunedain, descended from Isildur and Elros and the heroes of old. Arwen returns to Rivendell and meets Aragorn, who falls in love with her. Elrond informs Aragorn that he will not marry until he has achieved his destined goal - reclaiming the throne of Gondor.
Season 7: ???
I definitely do see a value to breaking up the Season 6 Frame material. We could have the Season 5 portion focus on Estel learning that he is Aragorn, heir of the heroes of old, and tie that in to the destiny of Men in Middle-earth. He can revisit the Dúnedain. No appearance of Arwen until Season 6 (if we'd like). Or tie in the meeting with Arwen to the Andreth/Aegnor bit, as that is late in Season 5.
I think we'll find that the Aragorn and Arwen story doesn't actually parallel the Beren and Lúthien story very closely at all

Aragorn falls in love; Arwen doesn't. She pretty much views Aragorn as a young kid at this point. The closest the parallel comes is the part where Elrond says 'quest first, then marriage'. But that's late in the Aragorn/Arwen in Rivendell story, and early in the Beren/Lúthien story. The point in the story where they actually get engaged (50 year old Aragorn visiting Lothlórien) is the part that makes it look most like Beren/Lúthien.....and Aragorn very certainly does all of his 'Thorongil' questing alone and without Arwen before we get there.
And no talking dog
So, yes, while we have talked about having the '20 year old Aragorn meets Arwen in Rivendell' story be the Frame for Season 6, it's probably actually going to be rather challenging to make that happen! It was suggested that his mother Gilraen could be using Beren/Lúthien as a cautionary tale, and Aragorn goes ahead and finds it inspiring.
So...if we don't return to Aragorn right now, what are our other options?
We could have a Shire-centric Frame. Bilbo was our main character of the last frame, and we left him journeying through Mirkwood on his way home to the Shire. We could start off with him revisiting Rivendell, and then going on back to Bag End. What could happen in the Shire to mirror the stories of Men? Well, probably births and deaths and marriages

It's too early to get the births of Frodo, Sam, Merry, or Pippin, but we can select events based on the Hobbit family trees.
We're looking at SR 1349-50, roughly. That's well about before Lotho is born...so perhaps the wedding of Otho and Lobelia is in order? SR 1360 is the death of the two youngest children of the Old Took (Mirabella [100] and Isengar [98]), which would be great for a story of mortality and generations...but is alas 10 years too late. Donnamira dies in 1348 (she is of course Bilbo's aunt). Merry's father Saradoc Brandybuck is 10 years old; Frodo's mother Primula is 30 (so almost of age, but too young to get married, most likely). Sam's family tree doesn't seem to have anything in particular happening in 1349-50, but his father is likely a gardener at Bag End now.
So, yeah, I don't have a storyline picked out or anything, but I would at least like to consider 'the lives of Hobbits in the Shire' as the Season 5 frame. It'll be challenging to come up with the Dagor Bragollach parallel, that's for sure!