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The documentation of list_plot3d states that it returns

A 3-dimensional plot of a surface defined by the list v of points in 3-dimensional space.

So this is not the function you're looking for. (Maybe there could be a more helpful error message, though.)

Instead, plot individual points with point3d and sum the plots:

colorbyheight = lambda (x,y,z): tuple(colormaps.autumn(z/50)[0:3])
sum(point3d(P, color=colorbyheight(P)) for P in biglist)

Here you want the argument of the colormap to range from 0 to 1 (I chose z/50.)