Meanings of illustrious lordship in English

By order of his most illustrious Lordship, the archbishop of Mexico:

Illustrious Lord, your servant and client kisses the hands of your illustrious Lordship.

Your Most Reverend and Most Illustrious Lordship's

'Moreover,' he remarked, 'what is it that your illustrious lordship wishes me to do?

I hope, by the grace of God and that of your illustrious Lordship, that I may shortly be delivered from this captivity.

After having written another letter which accompanies this, I received that of your illustrious Lordship which came in the ship "San Juan."

Your illustrious Lordship commands me to observe the orders given to Francisco Gali about the discovery of the route from these ports toward Nueva España.