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Lance is a Dragon specialust, not a Dragon type specialist. Draconic Pokemon are very present i the original Japanese cocepts, see Lance, Iris and Clair outside of the main games, in stadium they had Ampharos, Steelix, Tyranitar and Lapras, all Pokemon sharing draconic features and moves, same for Iris Archeops and Aggron for example. Lance itself is a champion like Iris and isn't restricted to use only 1 type, same for Steven Stone (mostly Pokemon related to his hobbies and profession and type affinity) , so far Wallace was the only exception to this.
Same for Agatha which has a theme based on mysteries and Agatha Christie in the English versions, see the relation between Poison types and mansions from her romances? It's a theme involving creepy Pokemon, Karen most likely shares something with Agatha on her famy tree I swear, I think Karen is definitely related to witchcraft and femme fatale theme, has those aggressive but fascinaying Pokemon and that poisonous Vileplume for example, beauty and danger (her team was pretty shit in battle tho, the Stadium versions worked better on coverage and themes while preserving the original type specializations).