The lick on Muse's Madness from The 2nd Law record at 2:40 has piqued my interest. The love song starts gentle and then this lick kicks in, lighting the song up. Does anyone how the effect on this lick is created? Trying to give this a go to build up my skills.

I'm no expert on dialling in specific tones, but to me it just sounds like a more vintage 70s/80s lead tone. Reminds me a lot of Queen. I imagine a Fender or Vox amplifier was used for this one. As I said I'm no expert on these things, but it's by no means far along Matt Bellamys spectrum of crazy guitar sounds
As far as the sound goes, the above post covers it well, I immediately thought of Brian May / Queen.
If you want to know about licks or what he's actually playing, then the one interesting lick is the one halfway through the solo. It's played with a '3 on 4' pattern - groupings of 3 notes played in 16ths, 4 notes per beat.
It's a bit of a finger twister but not too bad, and you also have to watch out for skipping from the 4th string to the 1st and back again.
Like this :