Looks a nice car, but if you have only just bought it, please have a read of this.
A thread from a while ago about your car.
http://www.lexusownersclub.co.uk/forum/topic/86360-newby-requiring-info-on-my-possible-purchase/
Here you go.
http://www.ebay.co.uk/itm/Genuine-Toyota-Lexus-Tailored-Carpet-Floor-Mat-Single-Clip-Hook-New-Original-/251426637310?pt=UK_CarsParts_Vehicles_CarParts_SM&hash=item3a8a3205fe
The ones you have linked too are universal fit, Originals from dealers are only around £50 gbp for a full set of 4 and fit the contours of bumper exactly.
It's easy, pull the rubber grommet from door pillar and disconnect multiplug, Then support door and undo the bolts on the door. There is no messing around lining new door up as the bolts self-centre on re-fitting.
Every fault on modern cars has a code assigned to it, which is stored in the ecu they can then be read with an obd tool. That then tells which part is at fault.