Let's try simplifying the example.
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Latin Modern Roman}
\begin{document}
\addfontfeatures{LetterSpace=30.0}
AB CD EF
\showoutput
\end{document}
This is the relevant part from the log file when compiling with LuaLaTeX:
....\hbox(0.0+0.0)x15.0, direction TLT
....\EU2/LatinModernRoman(1)/m/n/10 A
....\kern 3.0
....\EU2/LatinModernRoman(1)/m/n/10 B
....\glue 3.33 plus 1.66331 minus 1.1111
....\EU2/LatinModernRoman(1)/m/n/10 C
....\kern 3.0
....\EU2/LatinModernRoman(1)/m/n/10 D
....\glue 3.33 plus 1.66331 minus 1.1111
....\EU2/LatinModernRoman(1)/m/n/10 E
....\kern 3.0
....\EU2/LatinModernRoman(1)/m/n/10 F
and here's the same when XeLaTeX is used:
....\hbox(0.0+0.0)x15.0
....\EU1/LatinModernRoman(1)/m/n/10 AB
....\glue 6.33 plus 3.16182 minus 2.1121
....\EU1/LatinModernRoman(1)/m/n/10 CD
....\glue 6.33 plus 3.16182 minus 2.1121
....\EU1/LatinModernRoman(1)/m/n/10 EF
The model used for representing letter spacing is different, so XeTeX doesn't show the interletter kerns. However, this shows where LuaLaTeX (or more probably luaotfload) goes wrong: in XeTeX also the interword space is multiplied by the spacing factor, which it isn't in LuaTeX.
Between the two letter groups we have
....\glue 3.33 plus 1.66331 minus 1.1111
in LuaTeX, while it is
....\glue 6.33 plus 3.16182 minus 2.1121
If I remove the \addfontfeatures line, the glue is the same in both engines.
If I change the font to Times New Roman, I get
....\glue 2.5 plus 1.24875 minus 0.83415
in LuaTeX (just like when LetterSpace is not added), but
....\glue 5.5 plus 2.74724 minus 1.83516
in XeTeX.
To make the bug clear: in XeTeX the amount of letter spacing is also added to the interword space, but this is not done in LuaTeX.
My suggestion is to use microtype letter spacing in LuaLaTeX:
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Times New Roman}
\usepackage{microtype}
\begin{document}
\textls[400]{AB CD EF}
\showoutput
\end{document}
produces
....\EU2/TimesNewRoman(0)/m/n/10/400ls A
....\EU2/TimesNewRoman(0)/m/n/10/400ls B
....\glue 3.5 plus 1.24875 minus 0.83415
....\EU2/TimesNewRoman(0)/m/n/10/400ls C
....\EU2/TimesNewRoman(0)/m/n/10/400ls D
....\glue 3.5 plus 1.24875 minus 0.83415
....\EU2/TimesNewRoman(0)/m/n/10/400ls E
....\EU2/TimesNewRoman(0)/m/n/10/400ls F
which is comparable to the XeTeX output and the result is

Here is a plain TeX example:
\input ifluatex.sty
\ifluatex
\input luaotfload.sty
\font\test=LatinModernRoman:mode=node;script=latn;language=DFLT;+tlig;+trep;letterspace=30
\else
\font\test="Latin Modern Roman/OT:script=latn;language=DFLT;mapping=tex-text;letterspace=30"
\fi
\test
AB CD EF
\tracingoutput=1
\tracingonline=1
\showboxbreadth=\maxdimen
\showboxdepth=\maxdimen
\bye
If run with LuaTeX, the output shows
...\test A
...\kern 2.7
...\test B
...\glue 3.087 plus 1.54195 minus 1.03003
...\test C
...\kern 2.7
...\test D
...\glue 3.087 plus 1.54195 minus 1.03003
...\test E
...\kern 2.7
...\test F
If run with XeTeX, it shows
...\test AB
...\glue 6.33 plus 3.16182 minus 2.1121
...\test CD
...\glue 6.33 plus 3.16182 minus 2.1121
...\test EF
so the problem is not due to interaction with LaTeX. If the letterspace bit is removed, the interword glue turns out to be 3.087pt with LuaTeX and 3.33pt with XeTeX.
fontspecin installed on your system? The reason I ask is that on my system -- MacTeX2015, LuaTeX 0.80.0, XeTeX 3.14159265-2.6-0.99992, fontspec 2.4e -- the outcome is the same when I compile your MWE under LuaLaTeX and XeLaTeX; what I get corresponds to the first of the two screenshots you've posted. – Mico Nov 03 '15 at 20:26SmallCapsFeatures={Renderer=Basic}, use something likeSmallCapsFeatures={LetterSpace=5}. There’s no need forRenderer=Basichere. – Thérèse Nov 03 '15 at 20:34\textls[200]{THIS IS A TEST}. – egreg Nov 03 '15 at 20:41LetterSpaceis broken in LuaTeX. – egreg Nov 03 '15 at 20:44\textls[200]{THIS IS A TEST}. I seem to get no change in the letter spacing. – NVaughan Nov 03 '15 at 20:47cpspfeature?Kerning=Uppercaseis not broken, and it may serve your immediate needs, though it’s very unlikely to give you as much spacing as you seem to want. – Thérèse Nov 03 '15 at 21:01microtypeway of specifying letter spacing. Remove the\addfontfeatureinstruction. – egreg Nov 03 '15 at 21:39microtypeinstead offontspec? – NVaughan Nov 03 '15 at 21:44\textls(pr\lsstyle, which is the corresponding declaration) it works, at least on my machine. – egreg Nov 03 '15 at 21:44WordSpace=3.0tofontspecor instead usemicrotype's\lsstyle[3000]{...}, right? Is this a bug? – NVaughan Nov 03 '15 at 21:50WordSpaceis not recommended. I said in a previous comment thatLetterSpaceseems to be broken in LuaTeX. But usingmicrotypefeatures seems to work. Don't confuse\textlswith\lsstyle. – egreg Nov 03 '15 at 21:59luaotfload, which is just making its way to CTAN mirrors today, seems to have fixed this problem. :-) – Thérèse Jan 25 '16 at 17:44