LEI has a set of tools that you can integrate into your application. It sounds like they'd be helpful in doing what you need here. There are a couple of LEI Activity types in particular that might be pertinent.
Replication Activities: When they run, they compare the data between two databases of your choosing. This can either be one-way (source to target), or two-way comparison based on a timestamp. You can set it to insert missing records, delete extra records, or update existing records that have obsolete data. It doesn't poll on its own, so you either need to use a Polling Activity (see below) or just run it periodically.
Polling Activities: This activity doesn't affect any data on its own, but is used to tell LEI when to launch other activities that do. You can set it to poll a database for specific changes. When those changes occur, you can set it to launch another activity that will take action (such as a Replication Activity as described above).
From what you described of your requirements, I think these two would be pretty useful activity types. You can read up on them in more detail, and browse the other activity types that LEI provides, in the LEI Activity and User Guide: