Liquidity mining is when projects that do not have their own Token (usually because they are a ChainLink dependency) decide to create a token that is used to make the product more efficient or get more users. The original usage was for the ParentChain and BabyChain Pairing, which was called Liquidity. The token Liquidity could be used on the parent chain or it could be sold into the market for other coins.
Liquidity mining is essentially a way to rent Liquidity because Liquidity is fundamental to the health of DEX's and most DEFi product. It's beneficial for both sides of the contract: for example, if the DEX itself requires Liquidity in order to operate, then it benefits from having it on its own chain. If only its users need the Liquidity (and not in order to operate), then they can mine it by holding their tokens, and later convert to other coins.
LN (Liquidity Network) was an innovative approach to solving liquidity at DEX's as second layer scaling solutions become more mainstream. LN allows you to easily leverage Bitcoin transactions and integrate them into any cryptocurrency protocol, this means that anyone implementing LN can use any coin that has LN support as a secure high throughput on-chain payment channel in between their customers and the LN node operators.