I've used two types of Ocean Optics spectrometers to look at various lamps' spectra and have found these closely match those provided by the manufacturers.I have a hard time believing that light spectra from LED's are any more continuous that those from MH's or T5's. From wikipedia:
A light-emitting diode (LED) is a semiconductor light source that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corresponding to the energy of the photons) is determined by the energy required for electrons to cross the band gap of the semiconductor.[5] White light is obtained by using multiple semiconductors or a layer of light-emitting phosphor on the semiconductor device.[6]
The band gap is an energetic transition of fixed and uniform magnitude (depending upon the materials used of course). While there is a small amount of spread in the wavelengths emitted from this band gap it's mostly monochromatic. And in the case of white LED's a phosphor is often used - this would act very similarly to a fluorescent lamp that uses a mixture of phosphors coated onto the inside of the tube that each emit monochromatically upon excitation with UV light. The greater the variety of phosphors used the closer the net emissions may approach a continuous spectrum, but it will never be anything more than a facsimile of a continuum.
None of the light sources we use over our tanks emit a true continuum as does the sun or black body radiation in general. That would require a filament lamp where the filament literally gets as hot as 10,000-20,000 Kelvin degrees! haha (and a gigantic tank cooler too!)
I suspect any spectragraphs provided by the manufacturers of LED's or T5 or MH's that show what appears to be a continuum are greatly smoothing that graph (i.e. lying). since the mechanism by which these devices produce light is by its nature discrete.