Claudia as a framework consists of multiple components. Claudia's deployment tool is theoretically compatible and can be used together with Laconia. Claudia's deployment tool is designed to be totally separate from its runtime dependencies, and Laconia is designed to be totally separate from its deployment tooling.
Claudia's API Builder, on the other hand, is incompatible with Laconia. Although both of them are trying to tackle a similar problem, fundamentally they follow a contradicting principle. Claudia's API Builder is focused on the web and encourage multiple HTTP endpoints on a single module. Laconia deals with not only web, and encourage one HTTP endpoint per function. Naturally, in a serverless architecture, you can use both of them together in separate serverless functions if needed. Do however note that Laconia features will not be able to be used in the Claudia Lambdas.