This conversion is one of those that we see all the time and I myself have probably asked enough questions regarding this as well to know enough about it. Basically, it comes down to looking at the utility versus driveability when considering not just the motor, but the drivetrain as well and how adding a M90 supercharger to an car that was not intended for it. First off, even if you did come up with a way to lower the boost (6 psi - 9 psi, instead of a SC's 13 psi) using a smaller pulley, you are still going to shorten the lifespan of the 3.8 L N/A. To date, I have never heard of anyone who has successfully managed to do this swap, which means there are probably a few reasons for it.
The 3.8 L, regardless of what many will say, is not a durable engine. Unless the whole bottom half has been rebuilt to withstand the additional strain of a supercharger, it will eventually go boom because it simply was not built to handle the strain than a positive displacement supercharger puts on the engine (crank snout and boost). A good tune is critical to maintaining a strong running engine, and though I may not know much about tuning the SC, I'm willing to guess that if you set it up to run on less boost but use the ECU in stock form, something will go wrong. I'm not positive but I also believe the piston design differed from the SC to the LX and the LX definnetly has hypereutectic pistons that won't like a lot of knock before they break into a bunch of pieces. What I'm trying to get at is that you would be better off taking another approach to getting more power than this conversion not only because you'll be on your own for figuring out what do, but also because it just isn't as viable as a V8 swap or a straightup SC engine swap. The 3.8 L N/A is not the 3.8 L SC and, in my opinion, should not be converted to run in SC form unless you're just looking to do an experiment and don't intend for this car to be a daily driver.
Aside from the engine, the rear end in the LX is a 7.5" as opposed to an 8.8" in the SC, which also has larger half shafts. It also has a stronger AOD transmission. Though some may contrast my thoughts on the 3.8 L N/A engine, I'm sure not many will contradict me saying that the AOD transmission is pretty crappy and does not take punishment well. This being said, I'm sure a great deal of how the tranmission holds up depends on the driving. However, the 3.8 L in N/A form was the weakest built one that you could get and after only 55,000 km of granny driving and then an additional 30,000 km of my 'spirited' teenage driving, mine was toast. With the additional torque of a supercharger, this transmission won't hold out for long. My point is that when you add the strain of a supercharger to the whole system that makes up the car, you will drastically increase the wear of all parts that incorporate it.
But enough of my rant. If you want some help in the right direction, explain exactly what you want out of this car and I'm sure many people on this forum will chip in with great ideas. However, in my opinion, this conversion will not be one of them.