In case others may not know this. In JPlay they have a registry setting for "Dedicated Core" and the default setting is equal to one (1). This setting has JPlay change CPU Affinities to give it a dedicated core. If you are using CPU Affinity settings with Process Lasso, JPlay will change them unless you have Forced Mode enabled. With Forced Mode there will be core changes made by JPlay then PL takes over and changes them back.
If you do not want this "thrashing" or changing of Cores, just set JPlay Dedicated Core equal to Zero (0).