Sure, investigators come to church because a neighbor has been a good example, or they like the attention from the missionaries or whatever, but the ones who keep coming around are looking for something: the burden of sin lifted,
some sense of the meaning of life- why are we here, etc. They’re not looking to be wowed necessarily, but it’s more like– what’s in this for me? In the best sense possible, of course.

But still probably not what you’re after, right?

Your versions, though, could include somewhat broader content than the missionaries cover, with additional scripture and illustration and whatever else is part of your teaching style. Since your investigator wouldn’t be the only one in the class, the discussion could be broader and deeper than he may have got with the missionaries. This would be something familiar, something that reassures an investigator that we’re consistent in our teachings (i.e., the missionaries aren’t sugar-coating what we believe), but it almost certainly would include something unfamiliar about the familiar subject.

I guess I’m really just repeating B. Russ’s suggestion, with the reassurance to you that you *could* have these lessons ready at a moment’s notice, and they *could* have a knock-your-socks-off quality if you had prepared and tried them out enough so that your delivery and organization were the best they could be, and your stories worked because you had knocked off the rough edges, and your scriptures were delivered with the spirit in part because you had memorized them and knew how to quote them with the right emphasis. A lesson that really communicates what prayer is, how it works, and what it can do would be more effective and immediate to an investigator than any lesson on the temple or church history or anything else too foreign to him at this stage could possible be.

The reality is that I am a tinkerer and explorer in this sort of thing–I hate leaving things like programs, procedures, and policies alone. I like starting from scratch and examining whether we do things well, or if we just do them. The important thing is that I naturally lean toward the starting assumption that things are just being done, and not done well.

The need for a lesson which can be given without preparation, and the need for a lesson which will knock peoples’ socks off, are typically directly opposed to teach other.

I think if I were to gather 5 lessons for first/second time investigators I would stick to:
The Godhead
The Atonement
The Restoration
Faith, Repentance, Baptism
Eternal Families

I know thats exactly the stuff they’re getting from the missionaries already, but while they may seem like very basic things to us, around which every lesson we’ve ever had has revolved, it might be a little harder to grasp the LDS nuance for an investigator, and just hearing them again from a different teacher might help them gain deeper understanding and appreciation.