Don't listen to these guys, it can be done but you have to be a master modder to do it. In no particular order, you will have to do the following:
1. You must use all the sensors on the existing engine. This will mean modifying parts to accept the factory LS sensors, or finding sensors to fit the engine you want to use that have the same outputs as the factory LS sensors. It's likely that Ford uses the same outputs across the board, so any factory Ford sensor should work. You may have to swap connectors on the wiring harness.
2. You must find someone who can do a deep modification on the computer. They must be able to set the timing, fuel/air mix, fuel injector constants, cylinder size, ect. And, you must be able to mod the computer to use a multi-bar MAP sensor. If this cannot be done, then you will need to use the computer that comes with the engine, the install TWO sensors where one did the job to keep the LS computer happy. This must be done to retain things like air conditioning and ABS. The third alternative would be to strip the entire wiring harness from the car, remove the ABS and airbags, and install manual air conditioning controls. Or a fourth alternative, install the entire wiring harness from the donor car along with the ABS hubs, airbag controls and sensors, ect.
3. You must build custom mounts to install the engine and transmission. You will also need to be able to modify linkages, and the cables must be modified to run the throttle blade and cruise. You must also find a radiator that will both fit the car and have the correct number location of water outlets. It would be easiest to use electric fans for this, and over in the V8 S10 world the Ford Taurus SHO fan has been proven to be able to handle just about any HP level thrown at it.
4. Since it will be almost impossible to find a manual car, an auto will have to be modified. In this you are lucky as the floorpan of all the LS cars (at least the first gens) will be universal. This means that the car will have the provisions for both auto and manual transmissions. If the Gen 2s did not have a manual, the floorpan won't have the manual provisions. This will mean welding in a pedal mount.
5. The driveshaft, rear differential and rear axle shafts will need to be upgraded. The OEMs won't build the parts to take more than the car is expected to make from the factory, with a little extra strength to prevent the car from breaking before the warranty runs out.
6. As the LS is a unibody car, you will need to reinforce the car with subframe connectors.
I'm sure there is more than this, but the work I've described will take a good 3-4 years for someone who works for a living and is doing the job in their home garage. If you have the money you can hire it all out and get it done a lot faster, but by the time it's done you could have just bought a nice supercharged Jag that'll ride better, get better mileage and likely still beat the modded LS.
I've also been considering a triangulated 4-link rear suspension and have been playing with the idea of a strut front suspension because the ride is a little too harsh for the wife, who got pretty messed up in a car accident and now can't ride comfortably in it anymore.