How could I replace the lamp on a regular projector for a LED lamp?
You'd need to provide brand and model of projector and bulb plus web links. 

What you need to know, at least, is ANSI lumen rating of projector and present technology and rating.

All that said, this is getting more viable but is not something attempted lightly. The fact (as you recount it) that available solutions are from unknown makers and that they don't work may be because the conspiracy theory re bulbs is correct, but may also tell you something re difficulty.

Modern data projector bulbs are often "HID" (High Intensity Discharge) technology which is also found in car headlamps. This uses a small arc in eg Xenon gas with extremely high voltages and control gear to operate. (Bulb resrike when hot may required 10 kV+). HID bulbs for automotive use MAY provide a chaper projector solution but also may not - they are also qite expensive - but not as bad as projector bulbs generally.

Assume you have a 2000 ANSI lumen projector. This used to be a high spec but now is only OK for home theater etc. Assume that 50% of your 'bulb' light gets to the screen. That may be optimistic. Modern leading edge higher power LEDs are approaching 150+ lumen/Watt delivered. More realistically if you am at an out-of-module level of 100 l/W you are doing OK. So the LED wattage needed = 


Power = lumen x 2 / lumen-per-Watt = 2000 x 2 / 100 = 40 LED Watts.


In production volumes you can get a good LED for say $US1.50 for a 5 Watt unit - maybe cheaper. So LEDs alone would cost say $12 at the factory door or a retail cost of say 4x to 5x = say $50. Add support gear and that is liable to be hundreds and you are back into HID bulb cost area roughly. 

BUT that&#39;s not a tiny die size. You need to mount these so they constitute a point source comparable to a HID so ideally you&#39;d pt those in a  package yourself. If not (mot f us have problems packaging LED dies ourselves) and you wanted to mount them using available LEDs you&#39;d probably be lucky to get under 3mm x 3mm LED positioning or for 9 in a 3x square say 9mm x 9mm. That&#39;s larger than a HID arc so the optics would not work so you are up for new custom optics to make a small linear (parallel beam) light source - a not modest lensing requirement. 

As well as &quot;just doing it issues&quot; you need high CRI (maybe mixed phosphors and special LEDs), good colour temperatures (links with CRI), drive electronics and more. 

You now have to cool it. LEDs cost$ (as above) a moderately large amount and yu want reasonable longevity. Say you opt for  heatsink temperature of 50C. You need this in a housing that raises ambient and you want to be able to run this in Phoenix or Sammerkand or Nairobi in summer (maybe not Stovepipe Wells) without trashing the lamp. Say a modest 30C ambient. So delta t on heatink is 50-30= 20 C. So heatsink need is 20 C / 40 Watt = 0.5 C/W. That's a VERY nice heatsink, unless you have to pay for it. You'll certainly want to go to some lengths to stop hot spotting near the heat source. Heat pipe quite possible. Mere liquid cooling to a secondary air cool possibly. Blown air in volume certainly as well or alone. 

Stop!

This is getting hard. There is a risk of these being ridiculously expensive and of having design issues and of overheating and breaking. Sounds familiar, no?

ie this is a demanding task. It can be done with existing state of the art LEDs and state of the art cooling and worse - but HID does a nice job and people are paying for them unhappily but as required. So it's a technology whose idea has just about come. Expect to see the great and capable Philips Gloeilampen Fabriken company who lost their way somewhat since starting 100+ years ago but who have now returned to being masters of their original field, come up with something suitable any year now. (They will label it Luxeon / Lumileds.). Cree will be there. Also Osram. Soon also Seoul semi. Nichia maybe (they can afford to live off the patents from the rest). HP under another name. Maybe Siemens under another name. And others. 

The chances of you successfully joining them with a cost competitive trouble free product at this stage is low.

Double Flying Horse brand will be there but the LEDs will fail very early, colour temperatures will be suspect, die matching marginal, actual light output down, unforeseen technical problems excessive. You can buy them now.