What are the potential security issues when running a Lightning Node on my home network? If I was to run a lightning node on my home network (and for example, not running the node through TOR), what should I worry about? 

Furthermore, what OS, settings and software should I use to minimize the threats?
This is not only related to Lightning but remains true for any critical application that you run on your PC when connected to your home network. If your home network is compromised then an attacker can possibly escalate privileges and compromise the machine on which your lightning node is running (as well as other critical applications). Lightning is thought to be analogous to how you carry cash in your wallet. It helps you make small transaction very easily while at the same time it is not the end of the world if you lose that cash from your wallet. Your major saving are stored in the bank, just like how you will use a hardware wallet to store your major Bitcoin savings. I can think of the below few cases at the top of my mind.

Send payment to any lightning node
Your lightning node has to continuously sign new commitment transactions in order to add incoming HTLCs and fulfill HTLC payments. As a result, the private keys associated with signing new transactions in the channel are exposed to an application that is continuously interacting with your home network. In case your machine gets compromised like we discussed before, your private keys are no longer safe. Thus, these keys can be used to send a lightning payment to any node that is indirectly connected to you.

Force close your channel
Since the transaction backups are kept on the machine that interacts with the home network, an attacker who has gotten access to your machine can use one of the transaction backups and broadcast it to the Bitcoin network costing you high fees as compared to a mutual settlement (in case you were the funder). 

Broadcast previous commitment transaction state
The attacker might also broadcast previous transaction state making you lose almost entire balance of the channel through the revocation transaction.

Force crash your node and delete backup files
Unlike bitcoin stored in an on-chain wallet, funds in the lightning network are stateful. If you do not have backups and your channel counterparty is non-responsive, you will likely experience permanent loss of funds. This could be slightly mitigated by using the option_data_loss_protect feature, but that heavily depends that your counterparty node is honest.

The best practice will be to keep your machine clean from any shady applications, use a reputed anti-malware services and do not give share your home network Wi-Fi password.