Overall, my biggest problem with .45 ACP has been accidentally over-expanding the mouth of the case prior to seating the bullet. I'm talking about a general tendency over 30+ years, not anything specific to a particular case/bullet combination. Actually, I've had more problems with Remington .45 cases, come to think about it.
I believe that the Lee FCD die is meant to perfect a FMJ load that is developed. For example, it is very useful to post-size a FMJ 9mm cartridge for feeding purposes, because 9mm is supposed to be tapered. If the Lee FCD is altering your effective lead load, then you shouldn't be using it. In all honesty, I have used the Lee FCD with lead bullets, and I have had very mixed results. It will tend to mess with the driving band (heel) of a lead 9mm bullet in most instances, but it is a good tool with lead bullets for straight cases like .38 Special and .45 ACP.
The Lee expanding die tends to over-expand when using the Lee Auto Disk effectively, at least in my opinion. I suspect that the Lee FCD may be a "solution" to that problem. I have had good results with the Lee equipment overall, but I have also had some major issues with certain cartridges and components. For example, the Auto Disk system will not work with Nobel-Vectan ball powders like SP-8, because the spheres are so small that they bind the parts. You need to use a conventional measure with these powders.