The lend token is the utility token of the aave platform
Burning: the aave platform issues fees which are partially used to buy-back tokens from the market to immediatly burn them, continously shortening the supply. There's a total supply of 1,299,999,941 tokens from which 2,335,918.566 (~0.18%) have been burned. The token burn can be initiated by any user - it's a simple smart contract call. On https://burn.aave.com you can find a user interface which allows you to initiate a burn call via any browser wallet.
The platform has 2 type of fees. From borrowers, a 0.00001% of the loan amount is collected on loan origination, from which 20% is used for referral integrators and 80% is swapped to the LEND token and burned. From Flash Loans, a 0.09% is collected from the loan amount, from which 70% is redirected as extra income for depositors of the protocol and 30% is split using the same 20%/80% model of the origination fee. There are also transaction fees for Ethereum Blockchain usage, these fees depend on the network status and transaction complexity. (quote from: https://docs.aave.com/faq/#what-is-the-cost-of-the-service)
Governance: there will be governance votes with LEND. You can find more information over there: https://governance.aave.com/