1080 for sure, that's in the name.  They're all the same thing folks, and I'll be darned if I can find any formal video specification referencing any of them, so they share that too.  Is it all just marketing BS?  No, but surely the confusion has been leveraged by some DCCTV manufacturers, resellers, and the like to their benefit.

Half of 1080P

That's the gist folks.  As you know the 1080P raster dimensions stored to disk are 1920 x 1080.  With 1080N, 1080L or 1080P Lite the raster dimensions stored to disk are 960 x 1080; however, all three are intended to be display at 1920 x 1080 (16:9).  Literally half the number of pixels per line are stored to disk.  That is the commonality I've found between all three of these recording resolutions. 

Half the number of pixels of 1080P means half the storage, half the bandwidth required, and while effectively more pixels than 720P, all three are literally half the effective quality of 1080P.

1080P Capable Camera Required

In order to leverage 1080N/L/P Lite you'll need a 1080P capable camera and a recording device that uses one of these "Oh so clever" storage resolutions.  They are not "standards", 1080N/L/P Lite, they're good marketing and simple math. 

Variables

Come on, you knew with no definitive standard and decades of confusion in the industry over storage formats and raster dimensions there'd be more variables.  "What if we trim 16 pixels from each side of the image to further reduce size, sort of like with 960H using either 960x480 or 928x480, or with 720x480 or 704x480?" To be clear, there is absolutely no reason to do this as we're not sampling an analog video signal and blanking is entirely moot, but it does save a tiny bit more space.  Yep, all three are sometimes stored 944 x 1080, essentially throwing away another 32 pixels per line.

Keep Doing You

Research the recording device.  Review published specifications.  Test derrivative treatments side-by-side.  Return to the scene to calibrate the aspect ratio, when feasible & necessary. 

Do me a favor though, if you stumble on any published specifications for these, please share.  Keep being great & doing great things, my friends!