What is the difference between Lost Technica 《秘奥義【ロスト・テクニカ】》 and Last Crest 《魔道極法【ラスト・クレスト】》?

Question

The terms Lost Technica 《秘奥義【ロスト・テクニカ】》 and Last Crest 《魔道極法【ラスト・クレスト】》 are quite ambiguous, since they are usually mentioned together with the explanation for being a member of Trinity Seven.

In chapter 17, both terms are used one after another near the end of the chapter. This is from just before Liese activated her trump card.

"To be a Trinity Seven means that you've acquired the Lost Technica in your particular archive." - Liese ^{[Japanese version]}

When Liese activated her trump card, and Sora (the human form of Astil grimoire), warned Arata about the magic being used.

"This is Avaritia's Lost Technica, the Last Crest ..." - Sora

"That's right. It's Baal Peor" - Liese

Then in chapter 19, the condition to be part of Trinity Seven is reiterated, but this time with Last Crest in place of Lost Technica:

"The Trinity Seven are the top class magi of each of the seven deadly sins, right?" - Arata

"Correct. We are the ones who have mastered the Last Crest of each archive" - Lilith ^{[Japanese version]}

I have two questions regarding these two ambiguous terms:

1. What is the difference between them?

2. Regardless whether they refer to different concept or not, does Lost Technica implies Last Crest and vice versa?

(Please back up your answer with primary sources, rather than secondary sources like Wikipedia or Wikia. You can use them as starting point, though).