I want to start learning about lightning network and try setting up a channel. However I don't know if I need to already be running a full node. I stopped my core client from syncing a while back.
Using LND, you can use the neutrino client (which is a lite client). Instructions are available here.
You do not need to be running a full node. As Antoine mentions, you can locate a full node that is capable of serving light clients (Neutrino specification). A testnet full node run by Lightning Labs is available here. However, if you are interested in learning and experimenting I'd recommend that you do run a full node as you will not be restricted by the availability/services of third party full nodes and you also won't be fully dependent on Neutrino which at the time of writing is an experimental light client. It shouldn't be a problem to resume syncing your Bitcoin Core client and depending on when you stopped it shouldn't take too long to catch up with the latest block (obviously dependent on speed of CPU and internet connection). The latest LND installation instructions are here.