Other then a one-way sync from the lds.org calendar to Google, there is no support for Google calendar. I suggest you import your Google calendar into the one provided by the church on lds.org and run from there. That's the only sync supported by the LDS Tools app.
Have you searched the Help Center? Try doing a Google search and adding "site:churchofjesuschrist.org/help" to the search criteria.
So we can better help you, please edit your Profile to include your general location.