As far as I know we have no indication that Lucius is capable of casting the Patronus Charm at all. Or are you referring to the scene where Harry teaches Draco how to send messages with it?
“That reminds me,” said Harry after a while. “Can we test my hypothesis about how to use a Patronus to send messages?” [...]
The trick—or so Harry hypothesized—was wanting to spread the good news, wanting the recipient to know the truth of whatever happy thought you’d used to cast the Patronus Charm. Only instead of telling the recipient in words, the Patronus itself was the message. By wanting them to see that, the Patronus would go to them.
Actually Malfoy sends his to Harry with a message.
As far as I know we have no indication that Lucius is capable of casting the Patronus Charm at all. Or are you referring to the scene where Harry teaches Draco how to send messages with it?
The latter. Wait why would Harry teach Draco a secret trick belonging to Dumbledore’s close circle?
He just came up with the idea independently.
Or at least he saw that it could be done and independently came up with how.