What model lockright?
Here are a few things to check. Keep in mind that some of the symptons you described may actually be somewhat normal for the cheaper lockright. In fact, I had the same issues on my wifes YJ with a 14 bolt and took the lockright back out due to issues. After a good discussion with the richmond tech support guy, he claims the following stuff might be going on:
Did you install the thrust washers that go in between the side couplers and the carrier? Those are VERY much required.
Did you install the new, hardended cross shaft in the carrier or reuse the stock one?
Springs installed correctly? I know they only go one way, so it's kinda hard to mess up.
Are your rear tires worn evenly and at the same tire pressure?
Bent axle? You can measure along the top and bottom of the rear axle, from the 'diff housing' where the axle tubes are pressed in and the backing plate for the brakes. Those measurement should be exactly the same. Top/bottom. Front/rear.
Axle shafts contacting the lockright? In other words, they *might* be a touch too long.
Worn carrier. I know that may sound a little far fetched, but after doing a lot of research myself, I'm replacing my wife's 14 bolt carrier with another before putting the lockright back in.
Hope this helps!