I've checked the software but it appears there is nothing mentioned about the API or a way to pull the logs out of the application. I've also checked the Help section, but there was nothing mentioned as well which means it doesn't support it.
As always, if there is another version or a prototype offered only to certain customers, it can be obtained contacting the developers. They are able to explain all there is about the missing features or requests.
You can do this here: https://www.lascarelectronics.com/contact-us/