The Lancer is a new type of Big Daddy unique to the Minerva's Den DLC. The Lancer's main form of attack is its Ion Laser, which will provide constant damage for as long as you're caught in it. As well as that it also has another move called the Ion Flash, which will temporarily blind you if you see it. Despite all of this, he does not deal as much damage as the other types of Big Daddies, so if you can finish him off quickly, you will not suffer much damage from it. He also suffers from the same weaknesses the other Big Daddies do, so whatever strategy from armor-piercing rounds, to using security cameras against all work very well against Lancers. Security Bots can easily be found all throughout Minerva's Den, which can easily be hacked. They are an absolutely huge help against Lancers, as they are immune to it's Ion Flash.
Using the Gravity Well Plasmid that is also new to Minerva's Den, you can lock a Lancer in place. Doing so will prevent him from ever being able to from moving around and effectively using Ion Flash against you, which will make him much easier to take down.