بسم الله الرحمن الرحيم
It is the etiquette of the Holy Quran to recite it in the state of wudhu, turning towards Qiblah, and in sitting position. One can read the Holy Quran in the mobile as well while maintaining these etiquettes. It is not good to recite the Holy Quran in lying position.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.