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It kinda depends on my much IR light your camera lens absorbs.
A certain percentage of the light produced by the lamp (whether it's incandescent or an arc lamp) is infrared light. This is the same as the radiant heat you can feel coming off of a fire, for example.
Whereas with the LED light almost all of the photons it's emitting are going to be in the visible band. High intensity LEDs do produce some amount of waste heat, but this is in the form of heating up the structure they're connected to. So not only do they waste less energy, the energy they do waste isn't shooting out the front in the form of IR.
To be clear, visible light also turns into heat when it's absorbed, but with the LED you'd just be shooting visible light through your lens, whereas with a lamp you'd be shooting the same amount of visible light (same lumen value) plus a bunch of IR. So in the latter case there's a greater total amount of energy flowing through the lens.
All of this is to say that an LED emitter of the same lumen value almost certainly has less of a potential to heat up your camera lens. I guess if IR just passed right through it (and none of it got absorbed in the glass or in the tube of the lens) then it might not be much of a problem, and you'd just be heating up your projection screen slightly more. But I don't know enough about camera lenses to say if that's the case.
Thank you so very much! This makes sense and answers my question perfectly.