What is the Purpose of an Electrolyte in a Galvanic Cell? I understand how a galvanic cell works and the purpose of erverything such as the ssalt bridge and the electrodes, however I don't understand why an electrolyte is required. For example, consider this scenario. 

I have a copper electrode in one beaker, connected by a wire with a voltmeter to a graphite electrode in another beaker. The copper electrode is immersed in water while the graphite electrode is immersed in lead ions. There is also a salt bridge connecting the two beakers. Now my question is, will there be a reading in the voltmeter?

I believe that there should be one since copper is more reactive than lead so copper ions will form while solid lead will form on the graphite electrode. However my school teacher said it won't work as there is no electrolyte in the first beaker. Why does it make a difference if there is an electrolyte or not?
Two issues are at play here. 

1) You will measure a potential without any supporting electrolyte. As soon as you have everything connected, a potential will develop. Because a self-respecting voltmeter doesn't require much current (ideally zero), the potential will be measured.

2) As soon as you try to pass any current, as comments have mentioned, that current has to be carried from the electrode through the solutions and the salt bridge. Without any electrolyte in the solution, the solution resistance will be huge(as Geoff mentioned) and the amount of current passing will be cell voltage/cell resistance. This will essentially limit the current passing through the solution to very low values.