Why is the Greek letter “lamda” (lambda?) used in the logo?
When you’re on a platform and there’s a ladder that goes down beside the platform how do you get on the ladder?
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It has to do with Half Life 1, kind of, it’s mostly because it looks cool but in the research facility that everything blew up at (Black Mesa) the Lambda building was an important plot point (though I can’t recall exactly what happened in that one, was that the portal testing area, I think the starting area didn’t have a name but it may have been that).
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Walk into it, trust me, it fells really weird and you think you’ll fall but you get used to it, if you DO fall whip around in mid air and move forward and you’ll latch on.
Okay, just looked it up, the lambda complex is the one that was doing teleportation research (given the technology that starts the game you can see how this is important), they teleported Freeman to the Alien homeworld of Xen (these are presumably, but not assuredly different aliens from the combine) to take out the big alien controlling all the minor ones, some of which were enslaved (you meet the vortigaunts yet? Yeah… be glad they’re on your side now, they hit HARD).
Because, in math and physics, lamda as a symbol is part of how you calculate a half life.
I think someone was overthinking it a little. 
Valete,
Vox Imperatoris
Both Jragon and Horatius are correct. You will both be rewarded with… cake!
And since Black Mesa was basically destroyed, the Lamda logo became the symbol of the resistance in HL2. The resistance being in large part started by the former scientists of Lamda complex.
THE CAKE IS A LIE!
help me…
No, it’s not.
It’s just that you’ll never, ever get it!
AHAHAHAHA!
W… wh… what are you doing? I I… e… wh… Congratulations, you just passed the final part of the test where we pretended we were going to murder you!