Lock a row (preventing editing) while row is open

Hi there, we have a scheduling Smartsheet that we're having some troubles with. Users are booking appointments in the below view, but since the row isn't locked out while this is happening, we're ending up with double-booking because two users overlap using the row.

We have multiple people in the sheet, so if two people are able to open a row with an available appointment, there's a chance of double-booking.

Is there an option for locking a row for editing while it's open? Or another workaround that could prevent this booking issue?

Thanks in advance, happy to provide any additional information as needed.