My personal advice is flamethrowers. His combination of high health (800), high armour and high melee dodge meant that was the only thing I found to be effective.
Flamethrowers do the special fire damage of 5-10 per hit, ignoring armour. They also do 133% health damage. Combined with the Vampire Lord's 300% damage from burn and you can get some very impressive damage on him.
If you hit with all 8 blasts from a flamethrower, the health damage ranges from 159.6 to 319.2 (8 * X * 1.33 * 3) where X ranges between 5 and 10. Keep in mind too that this completely ignores his armour. I had to figure out how to deal with Vampire Lords myself and was surprised at how great flamethrowers were.