Hi Claudia,
Fishing in Lanzarote is good all year round, being February, March & April the best months for giant bluefin tuna; whearas September, October & November are high season for pelagic species such as blue marlin, white marlin, dorado, albacore etc.
If you want to look for some sharks, I would recommend autumn and winter months, since it'll be easier to catch hammerhead shark by fishing with natural bait.