There are several free and open-source calendars available for Linux, Windows and Mac OS X. Here are some options you may find useful:
1. GNOME Calendar - a lightweight calendar application that is part of the GNOME desktop environment. It supports various calendar types including lunar/lunisolar and has an option to show 13-months instead of 12.
2. KCalendar - a powerful and flexible calendar application that supports multiple calendars, including lunar/lunisolar and 13-month cycles. It also includes various plugins for additional functionality such as Google Calendar syncing.
3. Calibre - a comprehensive e-book management tool that also includes a calendar module. While it is primarily used to manage books, it can be useful for those who need a calendar with lunar/lunisolar or 13-month cycles.
4. OsmAnd - a mobile app that allows you to create custom maps and offline maps. It supports various map types including moon phases, which may be useful for those who need to plan trips based on the phase of the moon. 

 Yes, there are some FOSS apps that can help you with lunar cycles and a 13-month, 28-day calendar. Here are a few options:

1. Calendars - Free Calendar & Planner for Android: This app has a feature called "lunar phases" which shows the current phase of the moon along with information about each phase. You can also set up lunar calendars to track the cycles.

2. LunaCal for Android: This is an advanced calendar app that includes a feature called "Luna" that helps you keep track of your menstrual cycle and other aspects of women's health, including fertility and pregnancy. It also has a lunar phase feature.

3. Moon Phase Calculator by Glyphics: This is a web-based tool that allows you to calculate the moon phase for any given date. You can also view the phases in different ways, such as a graph or chart.

4. Dark Sky Weather Forecasting App: This app has an option called "moon data" which provides information about the current and upcoming phases of the moon.

I hope this helps!