DMC-GX1 vs DMC-LX7

The GX1 will outperform the LX7 for your low light and DoF priorities with the right lenses.  With the standard kit zoom, you'll still benefit from the sensor size on the GX1, but to really make the difference large, you'll need a fast lens for the GX1.  But those lenses for the GX1 will cost you.  Worth it in my opinion.

GX1 is definitely a better choice for low-light photography. Take a look at this comparison to see the huge difference in sensor and pixel size:  http://www.digicamdb.com/compare/panasonic_lumix-dmc-gx1-vs-panasonic_lumix-dmc-lx7/

Larger sensor and larger pixels offer better signal to noise ratio and greater dynamic range. With the right lens GX1 is a clear winner for both of your requirements.