I've found that I average 1.2 - 1.8 lilith frag per level X battle. The variance depends on how many 50 frag drops I get. That is averaged over thousands of battles. I get between 2 and 4 event frags per battle. The more event frags I receive the fewer lilith frags that drop. The average widely varied if you only do 1 or 2 refills.

I also noticed that the 50 frags drop in groups then go for awhile before another drops. When I really participate in the event I try to scatter my battles throughout the day.