How much time passes between the moment an intermediary node receives an HTLC and the moment it forwards if to the next hop? At least what order of magnitude is it? Is it comparable with network-latency (tens to hundreds of milliseconds)?
Short answer: Yes network Latency is should be the dominant factor here. (I have not profiled it and I am not aware of benchmarks)
If you look at bolt 02 https://github.com/lightningnetwork/lightning-rfc/blob/master/02-peer-protocol.md#adding-an-htlc-update_add_htlc you will see that
update_add_htlc message including the onion and
commitment-signed message will have to be sent / exchanged. (
revoke_and_ack is for settling the htlcs) while decrypting the onion and producing signatures are computationally rather expensive operations (we should not forget encrypting and decrypting the lightning messages themselves according to bolt 08 and noise_xk) these operations even on a local area network should not exceed the time for network I/O.