Is the questioner sinful if he asks his wife about her prayer and she lies to him that she has prayed, while he knows that she has not prayed?

The fundamental principle is to have a good opinion of your wife. If she is righteous, then believe her and do not investigate whether she has prayed or not. If she is neglectful in her religious duties, gently remind her and establish a study circle at home for reading the Quran, Hadith (definition), and the words of scholars, to strengthen faith and obedience. If that is not possible, encourage her to attend scholarly gatherings and Quran memorization centers. If it becomes clear that she completely abandons prayer, then advise her and remind her of the danger of abandoning prayer. If she responds and consistently performs her prayers, then praise be to Allah. Otherwise, separating from her is better for you.