What is the authenticity of the hadith: "Whoever leaves a stranger in his household while he knows it, Allah will not look at him on the Day of Judgment"? And is it permissible to leave a guest at home when he is too lazy to pray at the mosque and go to pray, or should one pray at home?

The aforementioned hadith (definition) was not found in the references. If the time for prayer arrives and a guest is present, the host should instruct him to pray with him in the mosque if it is obligatory upon him. If the guest refuses, or if it is not obligatory upon him, it is permissible to leave him at home, provided there is no unlawful privacy (khalwa (definition)). However, if his remaining would lead to unlawful privacy, then it is not permissible to leave him, and the host must ask him to wait outside the house until he returns.