I'm afraid I don't know how to interpret Luv. How does one determine if a triplet is imaginary?
I've been ignoring the asterisks and the single quotes, but I'm afraid I'm going to have to get into that to answer your question. If this turns out to be TMI, I apologize.
The plot that you posted is not actually CIEL*u*v*, usually abbreviated CIELuv or just Luv (pronounced "love"). It looks to me to be L in the vertical axis, and u' and v' in the horizontal axis. u'v' is a chromaticity space like xy. It's derived from xy as follows:
u' = 4x/(-2x+12y+3)
v' = 9y/(-2x+12y+3)
u'v' is more perceptually uniform than xy, which, among other things, gives undue prominence to the greens.
In the Lu'v' space, to see if the triplet is visible, ignore the L value and just look at u' and v'. If that pair is inside the horseshoe, the triplet is a visible color. If it's not, it's not. Pretty simple, huh?
In CIEL*u*v*, the chromaticity components are reduced by those of the white point, multiplied by a constant, and multiplied further by L*, the same luminance component as in CIELab. This has the effect of making the 3D L*u*v* visible color gamut roughly conical, with the only possible u* value for a color with an L* of zero being zero, and likewise for v*.
That makes it a little harder to look as a L*u*v* 3D plot and see the limits of visible colors. If the tool you're using doesn't provide the option of plotting the spectral locus (and it looks like the Lu'v' plot did have that option, the best thing to do is include a bunch of points that define the locus. If you want, I can whip up an Excel spreadsheet with that data; you'll also be able to see the calculations. PM me if you want that.
In my own work, I used Excel or Smalltalk to generate the data and commercial 3D graphing tools (Mathematica works fine) to plot the graphs. Now, when I have to, which is not often, I do the whole thing in Matlab.
Now that I've said all that, I think there's something wrong with your Lu'v' plots, if that's what they are. Before I possibly waste my time, is that what they are?