I would say Yes, but maybe tight , Look at CameraSize.com, Got the dimensions there.
I can fit a GX1 with a Pana 25 f1.4
Nikon Coolpix L820 dimensions: 111x76.3x84.5 mm
Panasonic GX1 without Pana 25 us is 116.3x67.8x39.4 mm
Pana 25 is about 50mm making dimension of GX1 as 116.3x67.8x89.4 mm
Nikon Coolpix L820 is 5% (5.3 mm) narrower and 13% (8.5 mm) taller than Panasonic Lumix DMC-GX1.
Nikon Coolpix L820 is 114% (45.1 mm) thicker than Panasonic Lumix DMC-GX1.