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More or less, yes.
A LN payment usually takes by default 4 hops, but you can set to take more if you want.
Hops means, how many nodes will route your payment. Each node do not know too much about sender and receiver, that's called onion routing.
Let me see if I got this right. To keep this channel private, the route would be as follows:
A- My private node
B- A second node, either my own or a third party's
C- LSP
A and B have a private channel, and B has a public channel with C that wraps the payments destined for A. Is that it?