It would be very helpful to know what engine and trans you have in the J body... 93 would likely be a 3.0 V6, and either a 4 speed auto or a more rare, 5 speed manual. The J body Lebaron broke from the K car mold when it was introduced in 1987. While it shares suspension components and powertrains with MOST of the Chrysler FWD lineup, the chassis were significantly different. But yes, they have their roots in the K car, which was a very versatile platform.
To clarify, Chrysler used the same motors in many lines. But there are specific generations to be aware of.
Donovan's Dodge Garage has TONS of info on all Chrysler turbo engines.
If you wish to switch to a 4 banger, any 92-93 Shadow or Daytona should provide what you want, the 2.5 liter 4 banger, has a smallish turbo, great for spooling up at the low end, but runs out of juice at higher RPMs. A very common swap is to use the turbo off the earlier 2.2 engines. The turbo vans were from the factory in 89-90, both Dodge Caravan and Plymouth Voyager. Be aware that there was an impedence change in the injector drivers between 91 and 92 model Chryslers.
The 93 Lebaron is a slippery shape. Is it the coupe or the ragtop?