I have switched several times with little to no breakage. From lye to no lye, and now I'm back to lye. I've tried Revlon lye, Motions lye, Just For Me, ORS, Optimum no lye, Design Essentials lye, and for the past year I've been using Optimum lye. Now I wouldn't recommend doing all of that, but I can say from my personal experience that I only experienced breakage with the Just For Me relaxer, and that was because my friend ran it all the way through to the ends.
The only really negative side effect I've had from switching so much is extremely underprocessed hair. The last time I saw my old stylist she used some other relaxer on my hair and it quickly reverted. Other than that, I'm now strictly Optimum lye. HTH!!!