Setting up cloud database for syncing to local SQLite database
While CDC is one useful methodology in SQL Server, it can also be a little performance heavy too depending on how much data and how frequently it changes.
You might want to consider a 3rd party tool to manage your synchronization between SQL Server and SQLite, which can help minimize the performance and maintenance overhead of a homebrew solution.
For example SQLiteSync by Amplifier is supposed to work well for this kind of use case (note I haven't used it myself though).
https://ampliapps.com/sqlite-sync/