The required lumen rating depends on the optical efficiency of the original light fixtures. The major difference here is, the HID's are rated as the bulb alone, but part of that light get lost in the fixture when redirected to where it is actually needed. But with LED lanterns, the rated lumen output is measured already with all the optics (as it is integrated with the LED modules). This rating inconsistency creates a lot of mess and errors, when converting from one to the other, as the optical efficiency of fixtures is often nowhere to be directly specified (it is "hidden" within in the beam pattern diagrams), so it is hard to match the rating. It depends on how the beam pattern looks like, how the original lanterns performed,...
Plus on top of that is the way different aging profile (the way how each light source degrades over time) and the way how the lumen output is specified.
So I'm afraid you won't be able to match the light output exactly, so you would have to start from scratch: Get the required lightning level specifications, then go through the documentation of fixtures available for you to choose, calculate the illumination levels and try to match it with the requirement. Important note: When deviating from the specified level, remember the variation in the illumination is way more visible then the absolute light level. That also includes the light contrast with surrounding areas.
Fortunately the eye tends to register the light level as a log(light level), which means even when there is half lux levels, no one would notice unless having some form of absolute reference. So if you keep the pattern the same as it was (fixtures at the same places, with the same beam pattern) and the light output will be at least order of magnitude the same as it was (3000lm LED is very similar to 5600lm HID; when assuming some losses in the HID optics and the lumen depression of the HID, it will be very similar or at least not that far off), you are fine.
Remember, +/-30% in absolute intensity is on te border to be noticeable at all, but differences of 10% between two neighboring sections is pretty well visible. As the original (as far as I understood your description) was a bunch of the same model fixtures, the consistency won't be that difficult, when using again everywhere the same assemblies.
@dor: Yes, it would be probably better if HID fixtures would be available, but tat is not the case, so the only option is to use what is possible to get. And what will be supported even through the life of the installation. It does not make sense to install expensive HID fixtures now, when within 3 years the replacement lamps would be bare unobtanium.
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