Halftone spots are made from printer dots, and if you have a limited number of printer dots, typically 600 dots per inch, you can only achieve certain percentage spots at any particular lpi setting you choose because the printer only prints 100% or 0% of each of those 600 dots.
A really good reference on this subject is Real World Scanning and Halftones by Blatner, Fleishman and Roth from Peachpit press.
Most laser printers are also capable of printing only a handful of different screen values, if that , no matter what you tell them to do.
So does that also explain why when I printed in a sequence of 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 that the 20 lpi looks like the 1 lpi from my 1-3 print sequence? And that the 15 lpi looks like the 9 lpi from the 5-9 lpi sequence?
It seems that what you are talking about is the printer resolution and not the halftones of a color.
The two are related. Halftone spots are made from a grid (square in the simplest case, but rarely that in the real world) of printer dots. If all the dots are "on" (inked) in the grid, the halftone spot is 100%. All "off" is 0%, half on is 50%, and so forth. A 600 dpi printer at 100 lpi uses 36 dots (6x6) for each halftone spot, so you can have 37 steps in your halftone. Since most people can't see the difference in adjacent 1 % steps this is a good compromise screen value for the tradeoff between fidelity of detail and tonal range, and most lasers default to something in this range.
Imagesetters typically have resolutions over 2000 dpi and are therefor capable of a much broader range of values (remember, you can only have lpi values that divide evenly into the printer resolution because you can't have half a printer dot any more than you can have half a pixel in your image).
I have no idea what you are seeing in your test series, but it's likely the printer is not delivering what you think it is.