Does a transaction get sent to the Blockchain when you use the Lightning Network to send payment to someone you're not directly connected to via an intermediary node?
Yes, an intermediary node is involved in lightning network. An intermediate node knows the previous hop's identity and the identity of the next hop as well as the forwarded amount, the hash-lock, and the timeout value.
Businesses that invest in Lightning Network nodes may become hubs or centralized nodes in the network by having more open connections with others.
Read more here: 1.
Investopedia2.
Lightning network privacy