The only advice I can give you Linus is that the softly softly approach always works for me. Keep it friendly, calm, non-confrontational but be persistent and be prepared for a bit of a slog. And personally I find the involvement of third parties just gets peoples backs up. I would certainly not be mentioning court unless you have the absolute final word from Lexus or the dealer. I've never had to resort to that or even mention it and I've had two brand new cars replaced FOC and numerous quite major issues sorted by certain German manufacturers mainly by smiling sweetly and appealing to the other parties better nature.
On the face of it these items should have been replaced before you took delivery and if the facts are as you state then you should be able to reach agreement with either Lexus or the dealer. Don't give up on the involvement of Lexus themselves. After all, the much mentioned warranty attached to used Lexus is based on conditions set out by the brand not the dealer.