Lara is an unusual spelling here compared to Laura, and the spelling barely comes up in the actual game. It's a bunch of characters saying what sounds like "Laura".
Case in point: when Lara Croft dies in a game, they said that was "objectifying" her death, even though she's the main character. But when a male character suffers the same fate, it's not objectifying them because they main character is meant to represent the self, and of course wouldn't it be silly to say you objectified yourself? Prince of Persia deaths would be the example here.
So is the main character (the players avatar) of a series objectified in this way or not? They seem to be just bringing up examples to suit themselves and ignoring when it happens to characters in a way that doesn't sell the theory.
Hell, in Heretic 2 you can explode into meaty gibbets. Much more disgusting deaths than Tomb Raider, but I've never heard anyone say that that objectifies men ... it's the switch from 1st person to 3rd person which raised the gore levels for the MC, not the fact that Lara is a woman. Tomb Raider just came along about the time it became practical to have an animated 3PS game.
The whole "objectification" argument is too semantic for me, but I can understand someone thinking that the new Tomb Raider *fetishizes* the deaths. Lara is characterized as weak, struggling to survive - no problem yet, Far Cry 3 did the same thing - but then puts her through a variety of contrived, torture-like situations. Lots of graphical impaling, though also plenty of dashing and crushing. One of the first impalings wasn't even a death, but a necessary plot point... She escapes some full-body bondage only to fall on a piece of rebar which goes straight through her abdomen. Hmmm.
But actually I don't think the game was overly sexualized at all. It's more like kicking a puppy: It gets an emotional reaction from people. The exact reaction differs from person to person, but they seemed to be shooting for pity, then compassion, then admiration.
Of course some people will have a different reaction to a hot girl getting abused, but I honestly think they weren't the target audience. The immature hormonal demographic responsible for chainmail bikinis isn't into *that*, generally. The horrible experiences were a necessary part of the origin story the developers wanted to tell, and I think it really worked.
(So I can see why people would think it's sexual pandering, but I disagree)