What is the ruling on reciting a permissible piece of poetry or any other words to a sick person, as a form of testing, and is that considered lying to him?

There is no harm in reciting permissible poetry or permissible speech. Testing a patient to determine if their illness is real or merely an illusion is permissible if it leads to their benefit. Similarly, there is no harm in entertaining a patient by having them listen to enjoyable poems or stories.