On-chain scaling still required with Lightning Network? I'm wondering if/how Lightning Network relieves us of on-chain scaling on the road towards mass-level adoption. As I understand, payment broadcasts are deferred to the point in which the channel is closed, whereupon they are bundled and settled via consensus. Seems to me that although funds can be transferred hand to hand instantaneously, if we achieve global adoption, Lightning Network spends may still congest the mempool when they are finally broadcasted. 

Discussion on page 52 of the Lightning Network whitepaper DRAFT Version 0.5.9.2 (after this was answered):


  If we presume that a decentralized payment network exists and one user
  will make 3 blockchain transactions per year on average, Bitcoin will
  be able to support over 35 million users with 1MB blocks in ideal
  circumstances (assuming 2000 transactions/MB, or 500 bytes/Tx). This
  is quite limited, and an increase of the block size may be necessary
  to support everyone in the world using Bitcoin. A simple increase of
  the block size would be a hard fork, meaning all nodes will need to
  update their wallets if they wish to participate in the network with
  the larger blocks.
  
  While it may appear as though this system will mitigate the block size
  increases in the short term, if it achieves global scale, it will
  necessitate a block size increase in the long term. Creating a
  credible tool to help prevent blockchain spam designed to encourage
  transactions to timeout becomes imperative.
Yes, it would require on-chain capacity increases if there were a lot of channels being opened and closed as well as normal on-chain transactions. This need is directly referenced in the Lightning Network paper itself.