HoL

Hi all, I desperately need a bit of help. I've got a naked K2 which the gears are being really temperamental, sometimes I can flick through them nice & smoothly other times it just won't change - quite often after starting off it gets stuck in first but if I slow right down or stop it'll let me change.
From reading other threads so far I've tried:
Cleaning behind the sprocket cover
Fresh oil - which I then drained some so it's just over min mark cos it was still happening.
I was told today it was because the chain was dry so that's now lubed but the same guy who told me this said it would probably take a week to rectify itself.
Obviously I've got my fingers crossed to see if it works but I'm new to this & can't see how the chain could affect the gears?

So just after some opinions, could it be due to the chain? any other ideas? a little terrified of a big bill problem!