Honestly, we didn't give Lambert much thought the first time we watched Alien. She was whiny and cried a lot. Her death could only have been more inevitable if she had come with a tattoo on her forehead that read "Victim." The only thing that surprised us was that she lasted as long as she did. But on a re-watch, Lambert starts to look a little more important and a little less useless.
Also, let's face it: In this type of situation, most of us are Lamberts.
Lambert's main characteristic is that she is the most emotional and empathetic of the characters. On the one hand, this is not a characteristic you want in a crew-mate, since her emotions tend to control her. On the other hand, she's probably going to be the first one to look out for you in a tight spot.
For example, after Brett's death, everyone gathers again to discuss a new plan of attack, and Lambert has the following exchange with Ripley:
Lambert: Could he want Brett alive?
Lambert: Could Brett be alive?
Ripley: No. I mean, I don't think so. (Alien)
Of all the crew, only Lambert considers the idea that Brett could be alive; Ripley's befuddled response shows that she hadn't even considered the possibility. In a slightly creepier interpretation, you could also say that Lambert is even able to empathize with the alien, wondering what it might want beyond simple murder and mayhem.
We see Lambert's empathy even earlier in the film when she is aboard the derelict alien spaceship. Dallas and Kane's dialogue in this scene is analytical and scientific—for example, Dallas's quickie autopsy of the alien corpse or Kane's description of the cave filled with the eggs. Lambert, in contrast, gets all touchy-feeling, saying "I wonder what happened to the rest of the crew" (ibid).
That's Lambert for you: great if you want a shoulder to cry on, but maybe not so great if you want to survive an alien invasion.
Human, All Too Human
Lambert's excessive emotions makes her a foil to two other characters, Ash and Ripley.
Let's start with Ash. Ash is a robot, meaning he's entirely inhuman, he cares for no one, and he never considers the pain, harm, or fear that others might suffer as a result of his (or anyone else's) actions. Major contrast to Lambert, who seems incapable of turning it off. So, it's a nice piece of poetic justice that Lambert is the one to ultimately finish off Ash. After pulling Ripley out of harm's way, Lambert cattle prods Ash, permanently neutralizing him. Grrl power!
On the human side of the equation is Ripley. Like Lambert, Ripley does care about others (including cats). We see this when Ripley discovers the message might be a warning, and she instantly wants to go after Dallas and the others to warn them. We also witness Ripley save Jonesy despite the dangers of leaving the shuttle.
The difference between Lambert and Ripley is that Ripley can turn it off and act while Lambert's emotions and fear get the better of her, ultimately crippling her ability to do what is necessary.
Ultimately, Lambert's emotions lead to her death. When the alien confronts her, Lambert is paralyzed with fear. As Ripley hears over the intercom:
Parker: Get out of the way!
Lambert: I can't!
Parker: Get out of the way! It's going to kill us!
Lambert: No, I can't! (Alien)
The way the film is shot leaves it ambiguous as to whether Lambert could have moved out of the way—providing Parker a clean shot at the creature—or if the alien truly had her cornered. Either way, though, we know that that watching Parker's death left her traumatized and emotionally paralyzed. Unable to move, she's the next one down.
It's All in the Name
Look, no one ever said that a blockbuster sci-fi spectacular had to be subtle. Even without any other clues from the filmmakers, we can tell a lot about Lambert from her name. You know, lamb. Lambs are herd animals that survive by sticking together. They also tend to be timid and need a shepherd to protect them, lest they get gobbled up by a wolf or alien predator.
And look at Lambert: she's timid and needy and prone to freezing at precisely the wrong moment. Ultimately, she's a herd animal, too attuned to the needs of the group to save herself.