Okay here's a Google product forum describing the problem:
https://productforums.google.com/forum/#!msg/calendar/yy1HTCdWTCM/bAsnrvx_BwAJ
Basically, you can't reorganize your task lists in Google Tasks. Yes, you can organize the items within the list, but there seems to be no way of actually organizing which lists are on top and which are on bottom. Has anyone anywhere found a solution to this?
Best Answer
In September 2020, I noticed that the web client has added grippers to re-order task lists under the list selection dropdown once the mouse hovers over the list name. (The mobile version does not have this yet.)