Hello PhilippSchmid,
Here's an article that lists out the Supported and Unsupported Artifacts and are specific to the K2 for SharePoint application.
Please refer to the "Supported and Unsupported SharePoint List and Library Templates" section.
That list says that 'Custom List' is supported!
In our solution we define a list template with BaseType="0" (which is Custom List according to http://mirusp2010.blogspot.com/2013/03/list-template-id.html) and Type="15000".
I wonder if the K2 code checks the type, rather than the base type.
"Custom List" is a term used within SharePoint for the ability to take a vanilla list and bring in columns. It sounds like there might be a difference between a SharePoint custom and a list you built to bring in functionality.
Our custom list template adds a few columns, replaces the EditForm.aspx page, and attaches event receivers. It should all be compatible with the K2 application.
Using the Smart Object Services Tester I was able to add the BaseTemplate of 15000 to the approved list of list types:
1. Open Smart Object Services Tester
2. Navigate to the SharePoint site collection that contains the template definition
3. Right-click and open 'Edit Service Instance'
4. Add the line below to the 'Included Lists' field:
<Lists><list name="BaseTemplate" value="15000" /></Lists>
5. Activate the K2 application for an instance of a list with BaseTemplate 15000.