The ending of The Last Revelation, in which Lara is entombed alive and presumed dead. Yes, she does get better, but her presumed last words ("Good to see you again... Werner...") and Werner removing his hat in grief are still exceptionally sad... especially when one remembers the violent end to their relationship in The Angel of Darkness.
Chronicles opens with a statue of the presumed-dead Lara Croft, seen on a rainy day, surrounded by mourners.
Noted among these mourners are a couple who appear to be her parents. Naturally, one might expect parents to be among mourners at a funeral, if their child died before them. However, in the Eidos/Core continuity, it was noted that Lara was estranged from her parents. Imagine what that must've been like for them in that situation.
There is also the death of Admiral Yarofev. He is injured after the Spear of Destiny causes an explosion on the ship. He regrets working with The Mafiya in order to find it, and makes a Heroic Sacrifice to get Lara out, but not before imploring her to tell how brave his crew were to the very end.
Lara:(sadly) Goodbye, Admiral...
Made more poignant by the fact that Lara, normally a rather cocky, snappy, "everyone-for-theirselves" sort, is adamant about not leaving the Admiral to die alone on the ship. He manages to convince her, but she clearly feels mournful about it.
Young Lara losing her mother in Legend, and the revelation at the end of the game that Lara is responsible in the present for this, by being the voice in the light that her mother had heard all those years ago.
And to put things even worse, Lara finds her mother in Avalon turned into a half-thrall and Lara had to kill her mother all while stating "My mother is dead" that part always make me feel sad for Lara after taking all that time to find her mother.
The death of Larson in Tomb Raider: Anniversary. This was no big deal in the original, but the remake completely changed things with all the UST between him and Lara, accompanied by the way the scene is played with him reaching out to Lara with his final breath and Lara staring at his body in panic as she realizes what she's done.
Let's not forget that in their encounter immediately prior to that, Larson saved her life. And Lara killed him never even knowing that Larson had "accidentally" knocked the Kid aside before he could shoot Lara in the back and then deliberately missed with his own shot.
Not to mention that if you fail any of the quick time events against Larson, he sounds genuinely regretful that he's hurt/killed Lara.
Made possibly worse by the fact that, in this continuity, he's implied to have been the first human Lara's ever had to kill.
Alister's death in Underworld.
Many times, though it's made worse if Lara is also crying.
The death of Roth and Grim given they go out saving Lara, and also Alex though it's played more for melancholy than tragedy. Roth's death also leaves her alone without anyone on her side, as up until that point he'd been her only help.
When Lara kisses Alex on the cheek before running. Doubly so if you found his (more-or-less unmissable) journal entry that reveals his massive crush on her.
The first time Lara kills a man and the trauma she goes through.
Hell, pretty much everything Lara goes through. Of course, halfway through the game is around the point she stops putting up with the island's shit and starts paying it back everything it's dished out, but when that happens (particularly evident by the exchange she has with Reyes where she responds to a What the Hell, Hero? with a jaded acknowledgement that she's come to accept all the death happening around her as "normal") you'll want to hug her for differentreasons.
When you reach the Survivor's Beach section of the game, you'll find a document written by Jonah. It says how his father would go into fits of rage and how he and his brother used to have to hide from his wrath. During these times his brother would tell him of Pania of the Reef. He then states that his brother had returned to Pania, implying that he swam out to sea to drown. Jonah then goes on to say that if he's the last one left he'll go to Pania too.
More of a Fridge Tearjerker, but the Enemy Radio Chatter (if you hold off long enough to listen to it,) does a pretty good job of showing how a good number of the mooks you will wade through are reasonably ordinary people just trying to survive a hellish situation. Also, as you kill mooks you can occasionally hear another mook shout "Brother!" in horror as his comrade dies. It's somewhat ironic that most of the people she mows down are a lot more sympathetic than the first man she kills, even though he's the only one she seems to be traumatised by.
Lara in the end. A boatmen acknowledges her wounds and the Thousand Yard Stare she has now. But most of all, she wants more answers and says she can't go home. She still has the research journal from the facility and indicates that she's going on more adventures. More than anything, this shows that she may have left the island, but the island has not left her. She can't go back to normal after everything she's faced and her entire life is going to be spent being purposely seeking out places which will put her in situations similar to, if not worse, than the island.