I think the Lee handles will work with RCBS and Lyman molds. Same prong thickness.
Most brands of handles work on most brands of 2-cavity blocks, except that Lyman/Saeco handles may need to be modified as described elsewhere on this site.
Lyman handles may have varied over the years. Lyman handles I purchased about 5 years ago appear to be identical to Saeco handles. They are very sturdy and comfortable to use.
I use both Lee and RCBS on a day to day basis. The RCBS is a little gentler on the blocks. The lead-behind-the-handle trick will make either handle close the block smoother.
One time I dropped a Lee handle on the floor and one steel prong broke in two as if it were glass. It must be some kind of cast steel. I welded it back together and it's still in use. OK, so Lee quality is not the greatest, but still, it's just a handle, and it does the job.
With any brand, and especially Lee, the wooden handles are apt to slide off. I've had good luck sticking them on with JB weld, after filing a few notches in the metal barb so the JB has something to grab hold of.