Disclaimer: I might be very wrong about things I have written because I haven't used lightning first hand. I have only read about it and these are the concerns I have about it. I would like you all to help me understand if I am wrong in any way.
Lightning network has come as savior of bitcoin to solve its speed and fees issue but I have many concerns surrounding it.
LN will lead to centralization: As more and more participants will join to enable sending a relatively large amount all the nodes in the route must have that much capacity in atleast one of their open channels. Not everyone has that many bitcoins to open several channels so the network will eventually contain hubs that have an open channel to lots of other. These hubs can then act as a point of failure.
Opening a channel is costly: Yes the LN does enable quicker micro transactions with less fees but for that you first need to open atleast one channel and that in itself needs good amount of bitcoin and fees to setup. A person with 0 bitcoin can't join the LN.
Opening channels is similar to bank deposits: You lock your bitcoins into an account and now to get them back you need permission from the other party. Suppose you open a channel with someone and you are in a net positive from the transactions over lightning on that channel. Now you urgently need to get those bitcoins back but you can't do that until the other person agrees to close that channel as well. The point is that to participate in the LN you have to loose the direct control over your coins on the bitcoin layer. This is just another form of bank.