Sounds like you have an organisational issue outside of that 15 minute window. In fact, likely, its because people are forcing your lead into meetings that are

Sounds like you have an organisational issue outside of that 15 minute window. In fact, likely, its because people are forcing your lead into meetings that are largely irrelevant (because otherwise if they permit that block to open they feel that wont be able to get time with them) that causes the lack of time in the first place.