For housing, all you need to do is replacing bulbs with LED counterpart as old bulbs fail. For stage lighting, you'll need to replace most of the equipment, not just bulbs.
A serious question from someone who has seen the lighting gear but doesn't really work in the industry - why would you need to do that?
I understand that the older gear uses various triac and even resistor (the really old stuff) dimmers which cannot easily dim LEDs. OK, so the dimmer may need to be replaced too. However why e.g. a console and the wiring to it would need changing as is being claimed? It is all normally controlled by DMX, no? (assuming a reasonably modern setup, not someone moving rheostats by hand to dim lights ...)
If the LED "bulb" has some sorts of "smarts" and needs digital control, I would only expect that there would be some sort of driver instead of the dimmer box talking to the console over DMX again.
Now I totally get that retrofitting an old fixture may not be cost effective (or even possible) and could cost more than getting a new one and that making the new hw work with the existing console/programs/whatever will be a pain but that's a different issue.
I also don't buy the arguments that the current LED-based (or other - e.g. halogen or something yet different) replacements are unusable because of different light output, fan noise, etc. Sure, could well be today - but that doesn't mean that will still be the case in two years time too. Especially if this kind of legislation comes into power, creating a large market for better lamps. If it will still be like that towards the end of that transitional period, sure, then there will be a legitimate issue and a complaint to be made.
@dmills has a lot of good points why tungsten lamps are still used in these applications, thanks for the illuminating (pun intended) info.