Koko the Gorilla seems to lie intentionally.

'She lies when it suits her. "Who broke the kitchen sink?" one of the staff asks her. Koko indicates another staff member, whirls about and starts to laugh.'

http://findarticles.com/p/articles/mi_m1252/is_12_131/ai_n85...

Even Alex the Parrot seemed to intentionally give wrong answers to questions when he was bored with a task.