It really depends. If you're an experienced seller on eBay or Craigslist, you will likely get the highest value for your LG phone on those platforms. However, they do require more effort from the seller, charge fees, and come with risk of fraud that novice sellers may not know how to protect themselves from.
If you share some of these concerns, we recommend using a trade-in site such as ItsWorthMore. Trade in websites leverage their volume discounts and industry know-how to provide a smooth streamlined experience; for a slightly lower payout.
Another alternative is to trade in your phone directly with your carrier. They typically offer the lowest payouts however, carriers tend to run promotions at times as well, usually if you switch carriers. Under the right circumstances, they can result in a very high return for your device.
Some older LG phones, especially non-functional ones, do not have much of a resale value and you can choose to recycle them. Recycling in an environmentally friendly manner helps keep toxic pollutants, such as lead, out of the environment.