I have a 2014 IS 350 and I really want to put a turbo on my car but I haven’t really found any kits for them. Is there a way to put a LS 500 engine which has twin turbo into my IS 350

 

Not really. It is a completely new engine compared to what is in the IS 350 and will not simply mate up to the transmissions on the IS 350.

I would recommend looking into RR Racing Supercharger kits if you're not dedicated to turbos. The only turbo IS 350 I know of is a one-off custom build.

 

Let’s say I did put an LS500 engine in it would I also have to put a LS500 transmission in it as well

 

I would assume so if you have a 6Speed AWD IS.
IMO The biggest problem would be the electrics, and getting the ECU of the LS500 to communicate with the IS ECUs. Also IMO; Cool project/Idea. Realistically, you would probably be better off trading your car in for a IS500, LS500, RCF, GSF, ECT. OR the RR-Racing Supercharger kit.
You would end up spending the same as the upgrade if not more doing a motor swap. And would end up throwing more money than your 14 IS is worth into it, only to end up with something that is un sellable and you would never get your money back... Unlike if you just upgraded to the more powerful car.

 

Ok awesome thanks for the help

 

it'd probably be cheaper to get a custom turbo set up then to do the eng, tranny and all of the above swap