No. The Lexus system is designed for limited functionality with Bluetooth. For example, if you have the 2011 Lexus model year, you can do A2DP bluetooth audio streaming to the stereo. You can use Bluetooth to call. SIRI is not a Bluetooth Function, so it is not going to work with your integrated car audio solution.
However, 3rd party solutions such as the Belkin Aircast Auto do work with Siri, they have designed it to activate your "voice dialing (aka SIRI)" function on the iPhone. They plug into your line in port in the center console, and work nicely with SIRI, you just have to make sure your stereo is on "Line" when you want to hear SIRI talking to you through the speakers.
For example, on the Belkin, this is how you activate it:
Make a call using voice-dialing:
If your phone supports voice-dialing, press and hold the Blue Belkin button until you hear your phone prompt for a command (about one second) .