Your first statement is correct, although you would only have to pay if you have no incoming liquidity.
In the second statement, in the case of wrapped invoices, the LSP does indeed know who you are when you receive payments. This has been a little trick before we had BOLT12 or BOLT11 with Blinded Paths.
And I have stuck to the Zeus defaults so that the user does not have to deal with the configuration.
However all these limitations will be removed by ARK.
I won't deny that monero has less friction than Lightning, but I won't deny that Lightning has even more privacy than monero well used, and as I said with ARK these frictions will be eliminated.
Monero offers good baseline privacy but there is still registration on the blockchain, you still have privacy issues at the network level, you have the problem of hidden inflation, and scalability problem that affects decentralization.