I believe that Pushing Buddies is supposed to quote both KEYGEN and Lancer's theme.
KEYGEN, in my opinion, is fairly obvious once you hear it. The melody on KEYGEN from 0:01 to 0:04 is very similar to Pushing Buddies's 0:00 to 0:03.
Lancer's theme is less obvious, but I still hear it particularly in the melody of Thrash Machine's 0:42 to 0:48 (and also a little in Acid Tunnel of Love's 1:00 to 1:10) to Pushing Buddies's 0:10 to 0:14.
I think the connection makes a lot of sense for Lancer, given that one of the song's appearances is in Rouxls' polyamory cutscene (Lancer's lesser dad). No clue why KEYGEN is quoted though.
I can tell what part you're saying sounds like KEYGEN, and it does sound a little similar, but the note timings are different and I don't see any reason these songs would be related at all. Seems coincidental.
The part said to sound like Lancer... I think I know what resemblance you're hearing? But also it's like, three notes and there's no clear reason why these songs would be related. Definitely coincidental.
I have conducted some research. For Pushing Buddies and Thrash Machine (image 1 and 2 respectively) they both ascend the chord at the beginning, and both follow the same exact rhythm with the same keys within the same (relative) chords at the end. Thrash Machine just has a little more flair in the middle, which I think was removed from Pushing Buddies to make it better match the melody of the beginning of the song.
Acid Tunnel Of Love is... dubious, now that I look at it. It's just a different variation of the same bit from Lancer's theme that Thrash Machine is riffing on here.
I'll share what these sound like as soon as I remember a good audio sharing service.
Here you will find my comparisons. Also, I've included an updated image of Pushing Buddies because I had the first three notes wrong. Oops.
Also also, I apologize for how rough Acid Tunnel of Love sounds. The entire song is detuned by ~50 cents, and I had trouble getting it tuned quite right.
