To Recite the Noble Qur'an While Lying Down
Question :
Is it permissible for me to read the Noble Qur'an from the Mushaf when I lie down on my side or on my back?
Answer:
Standing, sitting, walking, jogging, riding a car, lying down you are permitted to read the Qur'an in any of these positions. Nonetheless, it is better for you to read when you are seated, facing the Qiblah, understanding what you are reading, and contemplating its meanings in this way you completely benefit from your recitation.
Source:
Ibn Jibreen.
Fatawa Islamiyah, Vol. 7 Pages 20-21