4 ideas
Lucia jealously guards her recipe for Lobster à la Riseholme, and Mapp sneaks into Lucia's kitchen at Grebe to copy it. A flood hits while both women are in the kitchen, and they are carried out to sea clinging to an upturned kitchen table. Tilling presumes them drowned and holds a memorial service, but they return months later, rescued by a trawler, with their rivalry fully intact.
In a closed social circle, a possession or skill gains its value from being exclusive, not from being useful. Lucia refuses to share her lobster recipe because giving it away would turn a mark of superiority into common property. The rival's attempt to steal it is really an attempt to cancel that superiority, so a trivial secret can drive extreme behaviour.
View parties, invitations, and generosity in a small community as moves in a struggle over who sets the social calendar. The person who hosts most lavishly defines the terms of everyone else's social life, and guests become obliged dependents. Lucia's rapid round of entertainments after arriving in Tilling is conquest disguised as kindness, and the social world reorganises around her.
Where people have leisure but no real stakes, trivial rivalries supply the drama, purpose, and conversation that the community otherwise lacks. Onlookers take sides and gossip eagerly, and even the combatants need each other. When Mapp and Lucia are presumed dead, their feud resumes almost immediately on their return, because the conflict itself had become the point.