There's gotta be somewhere you can put it. Can you provide dash pictures?

See if you can poke around the internet and find other Lexus owners and perhaps even a Lexus BBS where you can ask other people how they installed an aftermarket stereo into their Lexus.

You might have to pay an installation shop extra to custom-fabricate a dash panel or something, but there's gotta be a way to get it into the dash. The question is how much trouble are you willing to go to?