This is about Lucy but bear with me. I think one of the most important arcs in fairy tail was the sun village arc. In it, we are introduced to the law of retrogression magic, a magic that makes mages and their magic less mature; and we see that Atlas Flame seems to recognise Natsu as END, or at least his fading memories of END are jogged when he sees Natsu hovering in front of him with "wings" and looking much more demon-like than usual. This reminds Atlas Flame that Igneel fought END in a great battle 400 years ago. As we now know that Natsu is END, at the very least Natsu's memory was altered when he travelled to the future. Also, if Natsu/END was a child when he went through the eclipse gate, he would neither have put up much of a fight with Igneel when he was 4, nor would a full grown present day Natsu remind Atlas Flame of the miraculously powerful child-demon of 400 years in the past. One explanation is that the law of retrogression was cast on the eclipse travellers, either to aid their integration into present day Ishgar, to protect them from Acnologia by diminishing their magic or to resolve some sort of conflict between them when they arrived. This would explain why Wendy, Rogue and Sting were ridiculously young when they started out alone in the new world.
Similarly with "Lucy", who is surrounded by clues that she has a long back story. The CSK refers to Lucy as "old friend" continuously, the celestial spirits seem to instinctively know her/can arrive without being summoned by her/want to avoid hurting her; she can cast mighty spells even with little apparent power and she has a very close platonic relationship with a dragon slayer. If she is Anna and arrived with the dragon slayers, she must have also been turned into a child and had her memories altered to protect the secrecy of the mission.
An argument against this is the traditional interpetation of Fried's enchantment in the battle of fairy tail. It prohibited passage to those who were over 80 and should have stopped Anna/Lucy, but we know that enchantments are very strict in their exactness. The enchantment did not stop "anyone born more than 80 years ago" from passing, but simply those who were over 80. Since time travel by its definition would seem not to alter one's age, I think it is more likely that the two eldest dragon slayers (Gajeel and Natsu, both of whom look a little less than human) were older than Anna before their regression and were thus blocked by the enchantment, rather than time travel changing the characters' ages.
The implications are wide ranging. It could mean that Lucy once had a relationship with Acnologia similar to her current one with Natsu. Also, that following the Beatles song theory of the names of Heartfilia reincarnations, that she is the one who gave Acnologia his arm ring and the "strength in his arms" which Igneel sacrificed himself to diminish and alluded to by Zeref. This would make her, along with Zeref, responsible for the genocide of the dragons, and the story of fairy tail, with all its scattered messages of forgiveness and redemption, could actually be a giant story of Anna's redemption for her part in this genocide and justify her role as the protagonist. It also creates a passionate and plausible reason for Natsu and Acnologia to fight over her in a legendary battle to be immortalised in that painting.
Quite long. I hope it makes sense.