Panasonic LX100 has a 13.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony A7 III's sensor provides 11MP more than Panasonic LX100's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the LX100 and A7 III sensor size comparison.
As seen above, Sony A7 III has a 3.8x Larger sensor area than Panasonic LX100. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Panasonic LX100 and Sony A7 III sensors have been tested by DxO and the results show that A7 III has a better overall score of 96, 29 points higher compared to LX100's score of 67.