Will my lenses fit a different body?

Only with corrective optics

Leica L sits 3.00mm further from the sensor than Nikon 1. An adapter can only add distance, never remove it, so infinity focus is impossible without corrective glass in the adapter — which costs sharpness and usually a stop of light.

Coverage & framing. Nikon 1 lenses are built for a 1-inch imaging circle, which is smaller than Full frame. Expect heavy vignetting or a forced crop on a Leica L body.