How can I test an iOS app with just a Macbook? I have a MacBook Pro and need to test my apps integration with another developer's iOS app. They have provided an installation link (itms-services://), but I don't have an iOS mobile device.

Is it possible to install and test their app on my MacBook with some sort of emulator?
Not really. Xcode has a simulator which cross compiles iOS source code onto the Mac processor. It’s not a proper emulator.

You’ll want some sort of cloud based unit testing or test lab service which getting a recommendation for is a little out of scope here. I’d budget a device testing library where you can rent devices (or perhaps take your app to the lab in question) or find a way to expense the hardware needed to test.