After Save Point 1 - Getting that darn purple key

[Lara]

otg wrote: I just played it to the first saving point [which has two pedestals... probably for a good reason?] and went up for the purple key. I get a feeling that the idea is to go not back, but forth, the same way, do a second save [so you don't have to do it again] and enter the room with the purple key again, this time with the grey door open! tadaa [haven't got the purple yet, just the second save... but now: off to the dungeon!]

Jackie's solution is much easier, but thanks!