Want to run REST API on-premise from Logic Apps

If you know about the following, could you tell me?

I want to run the REST API on-premise on the corporate NW from Azure's LogicApps.

ExpressRoute Opened Between Azure and Corporate NW

Is there anything else to be done from a network perspective?
Do I need to sign up for an Integrated Services Environment (ISE)?(I don't want to raise the monthly fee, so if there are other ways, I want to do it.)