Why can't I have more than 4GB of persistent data with LiLi?

This is a limitation of the FAT32 filesystem. When a drive is formated using FAT32, the biggest file that can be created is 4GB. Persistence is a file so it follows this rule.

There is a way to have a persistence larger than 4 GB. Read this FAQ's article.

Also have a look at: Why does LiLi only uses FAT32 and FAT filesystems?