If you have your own BMS, you can integrate it perfectly well with BeLazy, because you control it. The issue with tools like Plunet, XTRF and Protemos is that sometimes your own conventions and rules override the mapping logic, and have no place to be included in the system.
For example, if you don't want job deadlines to fall on a weekend, or if you would like to pay translation in words and review in hours, there is no easy way to make these changes. The variations are so wide that no user interface could bear every configuration option.
Plunet, XTRF and Protemos have APIs, but with the exception of Protemos, they are not easy to use. XTRF relies much on macros even for simple functionality, whereas Plunet's SOAP API is highly complex and has a very steep learning curve. The BMS Extension APIs are simple, unified API calls that perform certain frequent operations: they change deadlines, vendor assignments, price lines/financials, and list all the information available on entire projects. BeLazy monitors projects, tasks and jobs in all of the systems - these APIs shortcut access to them. Use them if after a correct configuration there are still things that a project manager manually needs to do in the commercial BMSes BeLazy supports.
While these APIs also work for the custom integrations and via Google Sheets, for third-party integrations the functionality is mostly interesting if the user has a commercial BMS.