It’s a different problem space. Lit seems very focused on the MPC use case. They are using some similar, albeit less strong cryptographic techniques, but at their core (based on https://developer.litprotocol.com/v3/resources/how-it-works) they seem focused on MPC, blockchain applications, and more social key distribution.

Juicebox is very focused on how does an individual user manage their private key for one service, in a simple and user-friendly way, without any compromise in security. Think like your keys for Signal, WhatsApp, or any other E2EE service. It could also be used to manage a wallet private key for a noncustodial wallet.

As far as I can tell, Lit also manages all the nodes available to you (even if they don’t personally run them). There’s not a freedom for you to run your own nodes. This is the most important thing for this kind of distributed cryptography to be used securely, and something Juicebox supports by default – all our server code is available on GitHub and we encourage people to host their own realms to build networks with appropriate trust characteristics.