When the channel is closed between Lightning Nodes, how is the closing transaction sent to the Bitcoin network? Does that mean to run a Lightning Node, you also have to run a Bitcoin node on your local machine since you have to broadcast closing transactions in the end? If there is a remote way for Lightning Node to communicate with Bitcoin Node, does that mean Lightning Node also has capability to communicate under Bitcoin protocol?
Lightning Channels are just unbroadcast cached Bitcoin transactions. So yes, Lightning Nodes need to keep abreast of transactions on the Bitcoin blockchain to notice new channels getting opened, existing channels getting closed, and need to be able to broadcast Bitcoin transactions to close channels or to submit justice transactions.
Different Lightning implementations use different ways to interact with the Bitcoin network. Some require access to a full node of varying flavor (e.g. Bitcoin Core, btcd), others use a light-client model based on compact block filters.