Hi @typosruinokes,
Sorry for the confusion! The download form at localbyflywheel.com currently serves Local Lightning as the default download. Local Lightning does currently conflict with MAMP and the one not in use will need to be stopped prior to using the other. We have plans to enable the two to work simultaneously in the coming months. 
If you need to run Local by Flywheel with MAMP simultaneously now, you can use Local by Flywheel 3.3.0 which can be downloaded here: Local by Flywheel 3.3.0