There are a lot of ways you could do this depending on your exact needs and what resources you have access to.
What kind of access do these applications have to your network? One thing we've done for some applications is just give them access to a network drive, then showed them how to build the XML import files.
Instead of letting them write directly to our repository, they drop in the network folder and we pull the files in ourselves; this gives us more control and allows us to easily scan things before it gets brought into the repository.
If you absolutely need an API, and you have developers, then you might want to use the Laserfiche SDK to build something yourself. Just keep in mind that the connection to the repository will need to be licensed in some way.