How can I make Zap synchronize with the Bitcoin network? I'm using the Mac operating system. I downloaded Lightning App and Zap from Github.

The wallet can not be synchronized with the network, how can I synchronize it and can I do it without having to download the full blockchain?

Lightning App shows me the error the network can not be synchronized...,
when I launch Lightning App it also pops up an error: Syncing to chain ... block height: 0.

When I launch Zap:

Uncaught Exception:
Error: Connect Failed
    at ClientReadableStream._emitStatusIfDone (/Applications/Zap.app/Contents/Resources/app.asar/node_modules/grpc/src/client.js:255:19)
    at ClientReadableStream._readsDone (/Applications/Zap.app/Contents/Resources/app.asar/node_modules/grpc/src/client.js:221:8)
    at readCallback (/Applications/Zap.app/Contents/Resources/app.asar/node_modules/grpc/src/client.js:283:12)


What am I missing to get Lightning to run?
To run the wallets you mentioned, you will need to also run a bitcoin node (bitcoind or btcd, most likely), and an lndnode as well. This information is listed in the README files on the pages you linked to. 

I believe there are lightning network wallets that work without a local full node, but I don’t have experience with one so you’ll have to dig a bit to find one that works for you. NOTE: without running a node on your machine, you will be trusting someone else’s node in order to use the lightning network.