The major risk of laparoscopic liver resection is still bleeding, specially from major hepatic vein. The bleeding from the hepatic artery and portal vein branches are well controlled by Pringle maneuver. Usually bleeding from small hepatic veins or tributaries are controlled with the increase in the pneumoperitoneum pressure but it should not be kept for a long time.The best way to avoid it is to perform anatomical liver resection, use intraoperative ultrasound to ascertain the liver anatomy and to prevent major vessels to be torn during liver transection. Pringle maneuver is also useful and I would reccomend to use it intermittently. Laparoscopic liver surgeon must have skills in suturing in order to repair major vessels rupture. Massive bleeding can be avoided with early conversion to hand-assisted operation or open surgery whenever hemorrhage control is not achieved.
Totally agree with Marcel again. To perform laparoscopic procedures more securely, the role of the anesthesiologist is paramount. Maintaining low central venous pressure helps to perform a more secure liver transection preventing injuries to vascular structures and to repair them if they occur. Here again, Pringle maneuver is important to operate in a bloodless field and to prevent vascular injuries.
Mikel raised an important point that is the role of the anesthesiologist in maintaining the low CVP to reduce bleeding. Really important, if any vascular injury occurs, keep calm and objective. If you rush to convert you may have an air embolism or a worst hemorrhage. Try to repair or at least temporary hemostasis with gauze before anything else.