I've heard all about HE-AAC, but I haven't read or heard anything at all about LC-AAC. Nero offers both choices for encoding, but I can't find anything in the Nero help files about LC-AAC. I did read somewhere, however, that low-complexity refers to audio encoding, and high-complexity refers to video+audio. So what does high-efficiency refer to? Suffice to say I'm confused.
look here (http://www.hydrogenaudio.org/forums/index.php?&act=Search&f=13), it's been answered a few times already.
short: HE - for low bitrates. LC - for medium and high bitrates.
further, see here (http://www.audiocoding.com/) for further details.
About current bitrates corresponding to tools/profiles
HE AAC = LC AAC + SBR
SBR is a tool that reconstructs high frequencies.