The biggest concern that I've heard, is that Lightning Network could become effectively centralized in the hands of whales that control the biggest hubs in which most transactions would occur.
Since im not a programmer, I don't really understand if this is FUD or a valid concern, and im still yet undecided about it. I've heard reputable people defending LN and i've heard other pretty smart people criticizing it. As a non programmer it's hard to know who is FUDding and who is being genuine.