Hi Katie,

I wasn't able to find information relating Laserfiche to Acumatica specifically, but I can provide some resources that might be helpful. I recommend checking out previous Empower presentations, which are available on the Support site. These presentations are related to using Workflow for integrations: Connecting Workflow to the World, Workflow Scripting and Custom Activities, and Advanced Workflow (slides 46-57 reference connecting to the web specifically). 

Additionally, many organizations have found Laserfiche Connector to be useful when integrating with web-based ERP systems. This Answers post gives some ideas. I hope this helps!