There is nothing wrong with reading from the Mus-haf whilst lying down.
Al-Bukhaari (7549) and Muslim (301) narrated that the Prophet (peace and blessings of Allaah be upon him) used to lie in ‘Aa’ishah’s lap and recite Qur’aan.
Al-Nawawi (may Allaah have mercy on him) said in Sharh Saheeh Muslim:
This indicates that it is permissible to read Qur’aan when reclining and lying down. End quote.
Shaykh Saalih al-Fawzaan said:
There is nothing wrong with reading the Qur’aan when lying down, whether one is lying on a bed or on the ground. There is nothing wrong with that. A person may recite Qur’aan whatever position he is in, standing or sitting or reclining, and whether he has wudoo’ or is in a state of minor impurity, if he is reciting from memory. But if he is reading from the Mus-haf, then it is not permissible for the one who does not have wudoo’ to touch the Mus-haf unless he has done wudoo’. End quote.
Al-Muntaqa min Fataawa al-Fawzan.
And Allaah knows best.