have you tried / considered a Factory Data Reset (FDR)? Many times that will help slow down & lag issues since it restores the phone back to factory settings, like the first day you bought it. Keep in mind, if you do a FDR, it will remove all apps that you installed from the Play Store and remove all personal files & settings. So before doing it, you should back up all important files, music, pictures, etc. somewhere other than the phone's internal storage. After a FDR, I usually just install the bare minimum apps that I need and see how things go for a few days. If the phone is running smooth again I start to add other apps a few at a time. I usually realize that I had a bunch of apps that I never really used and don't re-install them. A FDR can be a real pain sometimes, but once you get used to it, it can be a way to breath new life into an older phone and might make it smooth again.
Another option (I did this for my wife a few months ago when her RAZR M bogged down) is to uninstall every app that you have downloaded from the Play Store, clear the system cache & reboot the phone a few times in a row. Then, the same concept as after a FDR: just install the minimum apps that you really need & see how the phone runs. Then, install other apps & monitor the phone. This is still time consuming, but not as intrusive as a FDR.
Just some ideas that have helped me keep all of our phones running smooth.