I could be wrong but all App Services (Web Apps, Logic Apps, API Apps) are, by default, publically accessible and, by default, do not enable IP Filtering via Azure resource configuration (meaning, a setting on the Logic App). Options I can think of enabling this would be:
- If you have access to a Web.config, use an element to restrict traffic to only a specific set of address (see MSDN)
- Consider putting the Logic App behind an API Management resource and enforce a IP restriction policy (see Azure API Management Documentation); I'm guessing this may not apply for Logic Apps but including it anyway
- Scale to a Premium App Service Plan, deploy Logic App to an App Service Environment which gives you the ability to specify whether there is a Public IP (VIP) used for load balancing requests or internal load balancer (which would be used for cross-premise connectivity between your LAN and Azure); you can also deploy a virtual Web Application Firewall (WAF) which would allow you to place explicit IP filters as well
Not knowing your requirements, I'd lean more towards option 3 simply because there is documentation supporting that scenario (at least for Web, Mobile and API Apps -- Logic Apps are not mentioned). Otherwise, if you're not able to modify the web.config to include the filters and cannot put an API Management instance in front of the logic app, I'm not sure what other options you may have.
Hope this helps and if you find a solution, I'd be interested in learning it as well.