I've had 3 cars painted over the past 5 years, and to do it properly, you're looking at £10k plus. And that's for a standard colour, and a re-paint in the same colour.
To complete a colour change properly, there is a lot of work to be completed to strip out under the bonnet, the tailgate and the doors / sills. To do it really properly you'll have to drop out the engine and transmission.
Then there's the complexity of LY and as mentioned above, it's not an easy paint to get right.
I'd be surprised if anybody would take this on for less than £15k, maybe a bit more. So if you pay £20k for a non-LY Phase 2, add £15k onto it, you're in for £35k, for a car that many wouldn't buy because it's had a colour change.
I don't know how much LY cars are these days, but if your really can't have anything other than a LY car, remember that an original one will still be worth a premium in years to come, where a re-paint won't.
Mark