I did a search but never really found a definite yes answer.
My question is does the lady smith have the lighter springs already installed from the factory and if so is that the only difference between it and the 642?

No. It's only marketing and different markings.

I just put a Wolff 8lb hammer spring in and the 13lb rebound spring in. I can definitely feel a difference. Could their be any problems with using the 13lb rebound spring? Won't be able to shoot it until tomorrow.
Everything seems to be function fine.
Just asking because I had an sp101 that I put lighter springs in and the trigger was having trouble resetting. But that doesn't seem to be happening with the LS

Any time you install lighter springs, you need to test the revolver carefully. The springs you have chosen should work in a J-frame that is in excellent condition. But if anything is significantly out of spec, then there could be issues. For example, if endshake, headspace, or firing pin length are out of spec, then the lighter mainspring could lead to misfires. And if there are burrs, rough spots or friction, then there could be misfires or problems with return.

All of these problems are unlikely, but it is really not possible to say what springs will work without doing a thorough examination of the gun. If you test the gun thoroughly, it should become apparent whether everything is OK.