You may need to create a two-way iCal link to sync your LMPM calendar with a non-connected channel listing. This allows for the LMPM calendar to block the channel's calendar, and vice versa.
Please keep in mind that iCals don't auto-sync and run on a timed schedule. A double-booking can occur due to the lag in updates to the calendars.
Watch the video tutorial or follow the step-by-step guide to learn more.