Does the lightening network by any means require the use of mempool in transaction verification or it does byepass mempool?
Lightning Network nodes need to watch the mempool and the blockchain because they must:
a) check if their channel partner didn't cheat by broadcasting some old channel state (using a revoked commitment transaction),
b) check if any of the known channels' funding transactions have been spent,
c) check if a funding transaction for a specific channel has been confirmed upon receiving "channel_announcement" message.
When you send a transaction over the Lightning Network, you don't need to obtain any data from the mempool. Lightning Network nodes maintain a network graph of all channels so that they can easily and trustlessly calculate a path for the payment. Removal and addition of nodes based on the (un)confirmed transactions is a completely separate process.
