Assuming They are both Briggs engines, its a fairly easy swap. Couple things to look out for though. It the tractor is a hydrostatic the 12.5hp will be a little underpowered. It will still work. If you let us know what engine you have in the tractor and what engine you want to put into it i can walk you through it better. I’ve done 100’s of them.
It should bolt on fine if it's a Briggs 12.5hp. You'd optimally want a Craftsman style L-head exhaust to go with, otherwise you'll have to fab something up if you want to stay with the original muffler location. Cutting the hood and popping the exhaust straight out the left is a messier option.
If your 12.5 is an electric start made to operate with a battery (most likely), the charging system should be fine, as the LT2000 should not have an electric PTO. You may have to unhook the headlights (or convert to low-draw LED ran from the battery) if there's no lighting coil on the engine though.
That said, it'll be a bit under-powered for running the 42" deck, but might be fine if your grass isn't too thick, or if your don't mow too fast.
As was mentioned, a hydrostatic transaxle would exacerbate the power deficit over the original engine.
My 2 cents is that it should be fine. For about 99% of the time when I am mowing, the engine is loafing(14.5 Kohler Command 42" AYP/Sears). You can listen to the exhaust note and hear the times when the governor detects a slowdown and opens the throttle. I had an older Poulan 42"(AYP again) with a hydro and a B&S 13 and it also handled the load without problem.
I do not water, nor fertilize, and what grows it what grows. And it does grow, being a former cow pasture... 30-40 years ago. When it gets warm and we have rains, sometimes it gets out of hand as I won't mow wet 'stuff'. Then I have to slow down, but normally, the 14.5 handles without problems as a similar CV14 on a 33" snapper also does. They are not underpowered in the least, and the hydro Poulan did fine. Of course, conditions are local.