The modules shown on this page show 3 calendar modules using the Month Offset parameter.
To create additional calendar Modules - go to Extensions / Module Manager.
Select your Eventlistcalq module and then click on Copy.
This gets you another calendar module that you can set up with different parameters and settings.

Last Month uses parameter Month Offset set to -1 and also has Show Archived Events Only set to Yes

This Month uses the default parameter Month Offset set to 0

Next Month uses the parameter Month Offset set to 1.