I made a sample POC for integration of j2objc following http://j2objc.org/docs/Xcode-Build-Rules.html#adding-a-j2objc-build-rule. My POC works great but what I don't understand is I haven't added libz.dylib in Link phase and still it's working fine.By the way, I didn't add libz because I didn't know where to point to. As suggested on some other post copying libz.dylib from /usr/lib, didn't help. My POC is at https://github.com/vipu1212/MyConverter.
Your app doesn't have any references to java.util.zip classes, which depend on libz. It doesn't hurt anything to have an unreferenced library, so j2objc examples list all libraries its runtime depends upon to avoid link errors showing up as new developers experiment with it.