Both Panasonic ZS7 and Panasonic LF1 have 12.0 MP resolution sensors but Panasonic ZS7's sensor is 1/2.3-inch (6.08 x 4.56 mm ) and Panasonic LF1's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Panasonic LF1's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Panasonic ZS7.
Below you can see the ZS7 and LF1 sensor size comparison.
As seen above, Panasonic LF1 has a 1.5x Larger sensor area than Panasonic ZS7. 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.