The comedian's comments come as Lily's friend Robbie Williams is admitted to rehab for an addiction to prescription drugs, and Allen is in no doubt that his daughter is more sensible than many.
"There is no way she'll go to rehab," he simply said. "She's got too much of an old head on young shoulders - and she's seen from her parents the consequences when you drink too much."
Both Keith and Lily's mum Alison Owen have spent stints in rehab in the past, for addictions to alcohol.