Observations of Earth's magnetic field extending back to 3.45 billion years ago indicate that generation by a core dynamo must be sustained over most of Earth's history. However, recent estimates of thermal and electrical conductivity of liquid iron at core conditions from mineral physics experiments indicate that adiabatic heat flux is approximately 15 TW, nearly three times larger than previously thought, exacerbating difficulties for driving a core dynamo throughout Earth history by convective core cooling alone. Here, we explore the geomagnetic consequences of a basal magma ocean layer in the lowermost mantle, hypothesized to exist in the early Earth and perhaps surviving until well after the Archean. While the modern, solid lower mantle is an electromagnetic insulator, electrical conductivities of silicate melts are known to be higher, though as yet they are unconstrained for lowermost mantle conditions. We consider a range of possible electrical conductivities and find that for the highest electrical conductivities considered, a long-lived basal magma ocean could be a primary dynamo source region. This would suggest the proposed three magnetic eras observed in paleomagnetic data originate from distinct sources for dynamo generation: from 4.5 to 2.45 Ga within a basal magma ocean, from 2.25 to 0.4 Ga within a superadiabatically cooled liquid core, and from 0.4 Ga to present within a quasi-adiabatic core that includes a solidifying inner core.