When you sell/lease a channel, you will open the channel to the buyer who has paid you for the channel. Since they are buying from you this means they want inbound liquidity for themselves. When you open to them, you will have the outbound from the start. However they wouldn't be buying it if they didn't plan on using it so the channel should move more liquidity to your inbound side over time. Depending on the buyer this could be very quickly. You'll have to decide on a fee rate and if/how you want to keep the channel balanced based on it's profitability to you and the terms of your agreement with them.

They want to receive payments through your channel. They're paying you for their inbound capacity to them.