A Toyota dealership is actually able to repair your Lexus vehicle as the majority of the major systems are the same between Lexus and Toyota cars. Lexus cars will have higher end finishes but often the engines and other parts are the same or similar.
Unfortunately warranty services and recalls can only be done by an actual Lexus dealership. These are the only services that are provided solely by a Lexus dealership so you would have to go there to get them done.
All the new Lexus vehicles come with complimentary scheduled maintenance services the first 2 times it is needed. The first inspection happens after 6 months (or 5,000 miles) and the second one after 12 months (or 10,000 miles).