Sorry for the delay; I was having launch.
Cron plugin allows you to automatically launch both File Integrity and File Manager tasks when your server is not overloading, so you can maintain your QoS. Is not a MUST; you can launch them manually (the 'Memory limit' value is applied to the tasks; it doesn't matter if they are launched automatically or manually).
Your error is related to the amount of memory that this tasks need to store the data. If you have more than 150.000 files, you should increase the 'Memory limit' value , for instance, to 1024. In this case you can enable the Cron plugin and all should work fine.
If you have memory restrictions imposed by your hosting provider, you can't do much. You have to adjust the 'Memory limit' value and change the 'base path' (page 24 of the user guide) to a specific folder, so the tasks will be limited to this folder.