russell55 said:
In the case of the righteousness in Christ, I'd think the text is talking about the imputed righteousness of Christ.
But in 2 Peter, where the text parallels Lot's righteousness with his godliness, it'd be speaking of righteous behaviour. Or, you might say.....
fruit.
I'm not sure why you want to keep on maintaining that Lot had no fruit in light of this passage.

If Lot had fruit, it doesn't ruin your basic argument. It just means that Lot isn't one of the examples you can use.
I like what Dave Wilkerson says about Lot:
God called Lot righteous. Yet Lot had a deep spiritual problem: He was bound by an unseen cord to Sodom! The vile city had a hold on his heart. And Lot couldn't break loose from it, despite the continual decay of his soul: "For that righteous man dwelling among them, in seeing and hearing, vexed his righteous soul from day to day with their unlawful deeds" (2 Peter 2:8).
Lot knew better than to remain in Sodom. Scripture says, "Blessed is the man that walketh not in the counsel of the ungodly, nor standeth in the way of sinners, nor sitteth in the seat of the scornful" (Psalm 1:1). Lot should have decided, "That's it - I've got to get out of here! If I stay any longer, this iniquity will lay hold of me. It will cost me my soul!" But he never had the willpower to go.
God had already given Lot at least one opportunity to leave. In Genesis 14, we read that a confederate army of kings invaded Sodom and Gomorrah, looting the cities and taking the people captive. Lot and his family were among those captured (see Genesis 14:12).
When Abraham heard about the attack, he armed his 318 servants and pursued the invaders. And, through God's miracle-working power, he overcame those enemy kings and recovered everything: "He brought back all the goods, and also brought again his brother Lot, and his goods, and the women also, and the people" (verse 16).
Lot had received supernatural deliverance from Sodom. But instead of leaving the wicked city, he went straight back to it!
My late friend Leonard Ravenhill, the great prophetic man of God, wrote a book called Sodom Had No Bible. Indeed, Sodom had no scriptures - but that city did have one of the most powerful sermons ever preached to humankind. The sermon was Abraham - a godly man who stood for righteousness.
The people of Sodom saw Abraham worship, pay tithes and walk humbly before the Lord. And when he refused to accept a reward for rescuing their city, it was a loving rebuke to their wicked lifestyle. Abraham wouldn't accept even a shoelace from Sodom! (see verse 23). This godly man's example should have sent shudders through Lot - but it didn't. Lot still refused to leave Sodom. I've often wondered, "Why didn't Lot go? The Bible says he loved God. Surely he was concerned for his own soul."
Lot represents a kind of struggling Christian today. This believer has received by faith the imputed righteousness of Christ. Yet his soul is vexed by the sin he sees both in society and in his own heart. He knows he loves God. But something remains in his soul - perhaps a wicked habit or persistent evil thoughts.