How does lightning network find paths with sufficient liquidity?
Lightning Network nodes have their own P2P network where they send messages to each other containing information about their channels and their states. So a node will receive messages from the other nodes on the network that describe the available channels and their liquidity. So a node can build an internal map of the network's channels and the balances for each node in each channel. With this map, it can then plot a route for each payment.