Smashtasm/WMG

Lamp is from YouTube Poop
I mean, come on. In his flashbacks, he's interacting with a king in yellow and orange who rules Dinnertopia. Lamp is insane because he has been interacting with other insane characters that stutter. As well, Shipp even makes a reference to Hotel Mario AND Vegeta's OVAR 9,000 gag in his 9,000 Subscriber video.
 * In addition, Lamp even overuses a meme of his own in one episode. Lamp: IN BED! 1337f0x: Stop that!

Girem6 is Greg.
It seems fairly obvious, the name is an Anagram of IMGRE 6, or "I'm Greg", even though they say he might have died, I doubt that.
 * Word of God has already said he's gone. End of story.

Lamp's flashbacks are completely true.
I just realized how insane I am. But I think that Lamp's flashbacks aren't just his stupid fantasies, they all could be true, they could take place in a spam server, explaining how he knew what a spambot was.

Women are people.
That is why they wear socks. People wear socks.

Lamp is actually a woman in disguise
She just keeps this facade by changing her voice and adopt a new personality. She will possibly reveal her true gender in the climax of the series.
 * The only evidence you need is Samus does that.

Socks are the first sign that characters are real people who got sucked in.

 * Well, this would explain why Super64 didn't seem to like Lamp's Christmas gift. I mean, digital socks are utterly useless.

Lamp's change to full Cloudcuckoolander in season 2 is because Pimpachu isn't there.
Lamp was working for Pimpachu during Melee; given that Brawl Lamp is considered annoying in-universe, it's likely that downplaying that part of him (with the occasional leakthrough) was part of his employment terms. Since due to audience demand Pimpachu didn't join Brawl, Lamp's term of employment was terminated and as such there's no one imposing limits on him. The result is obvious.
 * PIMPACU, COME BAAAAAACK!!!! LAMP MUST BE TAMED!.....Sorry, couldn't resist.

King Kirb will appear in Season 2 as a minor character.

 * Ah, no. The creator has already confirmed he won't.

The whole thing-or at least Season 2-is Super64's dream
This explains why the series is so full of complete Non Sequitur scenes. This also explains why they take the form of video game characters-people commonly dream about fictional series which they have played/watched/read frequently.