Answer: "Graveyard" or "Cemetery" - Reasoning: Both "people lie" and "people sleep" are indications of many people using this place to lie down, or to sleep, which in itself is an odd thought. Crying and weeping indicate that this is a sad place, and the continued use of "people" allows this to mean not just those who are lying down or sleeping, but those who come to visit them there, (i.e. mourners). People come to ask the person grave why they did what they did that resulted in their death, as a form of mourning, or to ask their chosen God or Gods why they took that person to their grave. And peoples solitude refers to people sleeping on their own, or the mourners usually coming the mourn privately.
In this place, people lie, people cry, and people ask why. In this place, people sleep, people weep, and people's solitude, they keep. What is it?