To withdraw LP tokens from the outdated BASED-USDC vault, you will need to use the tombswap platform. On the tombswap platform, you can navigate to the 'Remove' tab and enter the details of the LP tokens you want to withdraw. This includes the token address of the LP token (0x04068DA6C83AFCFA0e13ba15A6696662335D5B75) and the address of the BASED-USDC vault (0x8D7d3409881b51466B483B11Ea1B8A03cdEd89ae). Once you have entered these details, you can click the 'Remove' button to begin the withdrawal process. The process may take a few minutes to complete, and once it is done, your LP tokens will be withdrawn from the outdated BASED-USDC vault.