How can I clean a lucite piece ?

Try cleaning with hot soapy water and a soft cloth. For the scratches, buff with eye glass cleaner.

Just soap and water. For the scratches, provided they aren't real deep, Mother's makes a plastic polish for cars. I love their products and use them for unintended purposes all the time.

Yes soap and water. Do not use glass cleaner or any cleaner with ammonia in it. Will make it cloudy.

thanks for that info and to avoid glass cleaner. hope that hadn't been done by prior owner. either way love the piece so will live with it!