Antiparasitaire can be an adjective or a noun, like "pest control" in English.
Un antiparasitaire (noun) is a product that will fight parasites and pests ("pest control product").
Lutte antiparasitaire (here the word is used as an adjective) is the fight against pests.
Lutte antiparasitaire can be used but I think in France lutte contre les nuisibles is more common (I guess there are regional variations, lutte antiparasitaire seems to be the usual term in Canada). In France if I walk into a shop to buy a pest control product I look for the Traitement contre les nuisibles sign.
Un expert en antiparasitaires1 is a person who is an expert in products that fight parasites and pests.
Un expert en lutte antiparasitaire is a person who is an expert in pest control (a pest control/management expert), I expect they know a lot more than just how to use the products, they probably do the actual job.
1 Plural, there are several products.