This is a really good and detailed question. First sentence: "If they had not concluded that it had been a lie, he would have been in trouble." "Had been" is correct here. You are describing something that happened before another action in the past (they concluded it). In English, we use the past perfect ("had been") to show one past action happened earlier than another past action. Do not change "had been" to "was" here. "Was" would not clearly show the two different times. Second sentence: "If I noticed that he were eager, I would do it." Here, "were" is a little unusual. Normally, we use "were" in imaginary or hypothetical conditions (called the "subjunctive" mood), like: If he were taller, he could play basketball. But in your sentence, "noticed" is not imaginary — it sounds like real action. So "was" would be better and more natural. Corrected version: "If I noticed that he was eager, I would do it." Summary: First sentence: Keep "had been." Second sentence: Change "were" to "was."