Can a voltage difference precede cloud-to-ground lightning, and can it be measured over a short distance?
There is always a background voltage difference from the ground up, of about 100V per vertical meter resulting in a net voltage difference of about 400,000V between the top of the atmosphere and earth ground. However, being a good insulator, makes for lousy conductivity, therefore the current density is extremely low which would make measuring with a common multimeter pretty hard: there's just not enough surface area on those tiny leads over which to contact air and ground. Add to that the very low current density, and your digital multimeter (DMM) is nowhere near sensitive enough to measure that voltage difference.

Although the moments preceding a lightning strike will generate a potential of tens of millions of volts, using a DMM still leaves you with a few big problems:

1) Lighting is an energy transmission that channels through a "pipe" of ionized air molecules. You'd be hard pressed to predict where that pipe is going to set up, getting there in time, and most importantly, surviving the instant supernova of steam that your body would turn into.

2) You're still left with the problem of the tiny surface area of DMMs leads. Sure, there's a big voltage potential, but the current density is still too small to measure with an unmodified DMM. Like Trond Hansen notes above, you'd need to connect your DMM to a large "collector" to actually see the difference, (then calculate the current density observed based on the surface area of your collector.)