The Mac project started in '80 when Jef Raskin had the idea to build a more "appliance like" and keyboard focused machine based on the 6809. Jobs horned in on the Mac project in early '81 and turned it into a much more expensive device that used features demonstrated by the Star.
The two teams were definitely separate and had little day to day communication with each other.
If the Mac was a "cost reduced Lisa" there would have been significantly more communication between the teams. And they probably would have said something like "The Mac is a Cost Reduced Lisa" in the Mac Business Plan from '81. Instead the business plan says they're distinct machines with distinct teams, objectives and target markets. [ See https://archive.computerhistory.org/resources/text/2009/1027... ]