I've put together a pretty large sequence using LRTimelapse 7. It's at 30fps and I did 4 on blurring.

But with, or without blurring, I get staggering in the clouds every 2 seconds in the middle of the video. Everything else looks good.

This isn't from the outputted video of LRTimelapse, but the final video that I'm editing in DaVinci Resolve.

Has anybody else seen this? Is DaVinci Resolve just pooh for this sort of thing?

Davinci Resolve should be fine. Maybe it's an incompatible Video setting.
Try using one of the Presets and force the crop to 16:9 in the LRT Render dialog and see if it happens again.

I played it with a lot more, and figured out that it was slowing down the clip to 96% that was causing the error. I even put it in Premiere and it did the same thing. I've slowed down my other time lapses in the past, not sure why 96% was a sweet spot to make it stagger/lag with the clouds. I was lucky that I had enough footage to do it at 100% speed, leftover with 3 seconds. o.O

What do you mean with "it" was slowing down? LRTimelapse can't do that. I assume, you slowed it down by that number in Premiere?

Yeah. I was using Resolve and Premiere to slow the footage down to 96% on a clip just over 4 minutes.

I'm not sure what that works out to, but it looks like it's lagging every 2 seconds. Only in the middle, when the clouds get critical.

I've slowed down other clips in the past, by 80% or so, and I've never noticed this before. It must be the combo of a long clip with a slight slow down that's causing this error.

Such "little" slow downs will cause frame doubling which might be visible.
Slowing down or accelerating should be used with care on any videos.