You need 2 pieces of information to connect your petition to Mailerlite; the API Key and the Group ID. You add the information in the dashboard > SpeakOut! > Petition > edit > 3rd Party Extras tab. This is a Pro feature.
Log into Mailerlite and in the top right corner click the drop down arrow next to your account name
Beside the Developer API item at the top, click Use
The values you need will then be revealed – assuming you have your group already set up
Copy them both into the SpeakOut! fields, update your petition and test.
NOTE: for this to work, you must enable the ‘Display opt-in checkbox’ under the Display Options tab on the edit petition page. i.e. you can’t add people to your mailing list without their permission.