1) The Lite version is not different in any way, except where it's "lite" and it'll tell you by asking you to buy ;)
2) I'll troubleshoot you through this.
All the information is helpful so far, but I need to clear up some things: when you say that MIDI Designer is able to receive: does a small, red LED light up in the top right corner of MIDI Designer? If not, it's not receiving. So that's first.
Then you need to download the app MIDI monitor, which is NOT by me, to figure out if IT can connect.
Thanks for helping out to figure this out. We will.