Is Lexus a Toyota

The answer is Yes,

Lexus IS the luxury brand of Toyota. Most parts for Lexus are the same for Toyota.

From the regular Toyota models its developers were challenged to created more luxury vehicle and that is when Lexus was developed. Lexus is more luxury category.

Some notable cars are:

Toyota Altezza is sold as a Lexus IS300

Toyota Soarer is sold as a Lexus SC300

Since 2005 Toyota Japan has opened Lexus dealerships in Japan.

It's the equivalent of Acura: Luxury Honda and Infinity: Nissan