I've looked into connector, but don't feel my answer lies in anything I've read so far. Rather than open a 3rd party application to open the actual document from the repository. Does Laserfiche have the ability export a forms data in something like XML, so another program can consume the data from a form into it's own data tables?
Example would be if the workflow put the file in a holding queue and sends a notice to the 3rd party program or the 3rd party program would monitor the holding queue. Then when there is a new form. A service request is sent to the 3rd party app for the data from the form. Then Laserfiche performs an export in something like XML to be consumed by the third party.