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Lindsay Lohan eating dinner last night at Cipriani Downtown with a group of friends (one of whom was hotelier Jason Pomeranc, left) ... Reese Witherspoon taking in "a business lunch with friends" at Cookshop on Tenth Avenue ... Jessica Simpson shopping with her mom ... American Idol judge Kara DioGuardi carrying gifts in Midtown ... Alexa Ray Joel posing for a pic outside The American Hotel in Sag Harbor alongside her mom, Christie Brinkley, and grandmother ... Maggie Gyllenhaal and Peter Sarsgaard wearing hard hats for Tuesday's dedication ceremony for the Signature Theatre Company's new Signature Center ... Catherine Zeta-Jones arriving at the Walter Kerr Theater on West 48th Street ... and Sarah Jessica Parker walking with Matthew Broderick in the West Village yesterday.