Yes, stored procedures use the same code as table lookup; so if the stored procedure takes a param it will monitor the field for changes before triggering.  So alter your procedure to accept a parameter like this:

Alter PROCEDURE [dbo].[sp_increment] 
    @notused varchar(50)  --added line
AS
BEGIN

Now add a new field to your form and assign it to 'notused'.  So now the SP will not be called until there is a change in the field.  

But that is not exactly what you asked for because you said you wanted to use a radio button not a input box to trigger the lookup.  Well lookup doesn't support changes in radio buttons to trigger a lookup out of the box.  You need to trigger a change event on the field. But this can be fixed with a little bit of JavaScript.

I added a class to my radio field called 'myradio' and when its clicked it fills the value into my 'notused' field which is linked to the lookup and triggers a change.

$(document).ready(function() {
  $('.myradio input').on('click', function() {
     $('.notused input').val($(this).val()).trigger('change');
  });
});

I then hide the 'notused' field with a a rule.