There’s nothing improper with lying down and reading the Quran from the Mus-haf.
The Prophet (peace and blessings of Allaah be upon him) used to lay in ‘Aishah’s lap and recite the Quran, according to Al-Bukhari (7549) and Muslim (301).
In Sharh Sahh Muslim, Al-Nawawi (may Allah have pity on him) said:
“This shows that reading the Quran while reclining or lying down is permitted.”
Shaykh Salih al-Fawzan said:
“There is nothing improper with lying down and reading the Quran, whether on a bed or on the ground. That is perfectly OK. If reciting from memory, a person may recite the Quran in any posture, including standing, sitting, or reclining, and whether or not he has wudu or is in a condition of slight impurity. But if he’s reading from the Mus-haf, it’s not allowed for someone who hasn’t done wudu to touch it until he’s done wudu.” Al-Muntaqa min Fatawa al-Fawzan (Al-Muntaqa min Fatawa al-Fawzan).
الَّذِينَ يَذْكُرُونَ اللّهَ قِيَامًا وَقُعُودًا وَعَلَىَ جُنُوبِهِمْ
“Who, when standing, sitting, or [laying] on their sides, remember Allah” [Al ‘Imraan: 191]
فَإِذَا قَضَيْتُمُ الصَّلاَةَ فَاذْكُرُواْ اللّهَ قِيَامًا وَقُعُودًا وَعَلَى جُنُوبِكُمْ
“And remember Allah standing, sitting, or [laying] on your sides once you’ve finished praying.” [Nisaa: 103]
This is due to Allah’s blessings, and He has made it simple for us, with the Qur’an serving as the most powerful reminder. So it’s not a sin to recite the Qur’an while lying down, and it’s also not a sin to do so when sitting. If he comes across a verse of prostration, he can either stand or sit and make prostration. This is because sajdah is a highly recommended sunnah rather than an obligation.
But….!!!
In the Qur’an, Allah Almighty describes real believers as follows:
“Such as remembering Allah when standing, sitting, or lying down, and contemplating the creation of the sky and the earth, (and saying): Our Lord! You did not make this for naught. All honour and glory to You! Save us from the Fire’s wrath.”