Katie Couric doesn’t live life like a rapper. The daytime queen declined a bottle of Cristal sent over when she dined at Old Homestead Steakhouse on Ninth Avenue. But Couric — who had stopped in for dinner with pals — did accept a lobster claw. After she admired a dish served to the table next to hers, its recipient “promptly ripped off a claw and gave it to Couric,” explained a spy. “The lobster guy then chatted it up with her.” But when more customers began to crowd Couric, staffers had to ensure she had privacy, even “rejecting another patron who tried sending her a bottle of champagne.” Meanwhile, we’re still reeling from her recent revelation that Larry King “lunged” at her during a bad date.