Tomb Raider: Legacy of Atlantis sees us return to what looks a lot like the original Lara Croft fans grew up with. It is a remake of the original game, after all, but that doesn't mean Crystal Dynamics is throwing away all the work it did before.
Speaking with IGN, Crystal Dynamics' experience director Jeff Adams said that this is the "same Lara," and that we're just finding her at a different point in her career. As the Survivor trilogy acted as a larger origin story for Lara, this new game will pick up with her as a veteran Tomb Raider, with a lot more confidence and flair to her personality.
If Legacy of Atlantis is going to be made canon to the Survivor trilogy, we can imagine that the new Tomb Raider: Catalyst will offer a similar continuation of that storyline. Legacy of Atlantis itself is a standalone adventure, but considering Crystal Dynamics has another Tomb Raider game currently slotted for a 2027 release, it wouldn't hurt for them to be interconnected in some way.