Thank you @ColinBarber for replying.
The Marshall dealer did the service and provided me with their approve warranty for a year - since this was not by Lexus, I missed out on the relax warranty. I went through the Marshall documentation, and it looks like the waterpump will be covered. My next service will be at Lexus which will activate the Relax warranty which should help me in the following years.
Brakes - sure, I will double-check the wear level. Lexus says it is between 3 - 4mm and needs urgent attention. The pre-delivery inspection report from Marshall says the wear is at 60%, I am assuming this should be around 4.5 mm, maybe? And for the worn discs, I can't really tell, got two visually shiny discs, but Lexus say they are worn, but I am not sure.
It sounds good, if the breaks could go for at least a year, I will get a few quotes. I have a local Toyota, will check their prices as well. Lexus quote came to about £450 I think, but I see prices with 50% less - not sure if this must be done at Lexus or elsewhere is fine.
Thank you.