Whenever I'm offline (which is pretty much all the time) and I'm using LiveSplit to time a run and I hit the split button to start a run or just split it takes about 2-3 seconds for it to actually split, I still get accurate times but it still annoying.
Sounds like you have split delay set. There's a setting/option somewhere in Livesplit that allows you to set a delay, it's to allow people to sync up livesplit with a delayed video feed from a capture card that has capture delay.
See if you have a value set for that as that could be causing this.
Either it's what Timmiluvs said or you have too many things open on whatever you're using livesplit on, I have this problem sometimes on my laptop and can be due to too much processing going on so when I hit the start key it takes a second or two to actually start and stop
ive already checked the delay number and its set to 0, and i never have anything else open in thee backround when i run unless im learning a new game.
You could always try to reinstall LiveSplit if you haven't already just in case to reset everything to default unless you've always had this problem