The link below that Sailvayu posted has something interesting and sort of related to grounding or not grounding
http://www.iclp-centre.org/pdf/Invited-Lecture-Rakov-2010.pdf
On page 6, there is a figure of a induced strike where they shot up a 150 meter conductor 400 meters high when it triggered a strike. Before the strike, the conductor has essentially no current flowing so it has a constant single voltage over its entire length and this is what concentrates the electric fields at either end and causes the leaders to form. Leaders form on both ends - even though there is no direct connection to "ground". This is important to note.. you dont need a conductor to be grounded to form leaders.
The negative leader is easier to understand as its electrons flowing in the direction of the leader. You might think the positive leader must be positive ions but really the positive current is still electrons - but they are flowing in the opposite direction of the progressing leader. The strong field at the very end of the leader ionizes the air out of ahead by pulling electrons from atoms which then travel downwards (assuming a negative sky charge). This leaves a positive charge in the direction the leader is traveling so looks like a propagating positive charge. As long as the field is high enough, this can continue by pulling the electrons off the atoms and the positive leader heads on upwards.
Another way to look at this is that when an air atom is ionized, there is an electron with a negative charge and the rest of the atom now with a positive charge. Both "parts" have the same charge so see the same force from the electric field. However.. the electron is something like 60 thousand times less mass so given the same force on both the electron and the ion (because they have the same charge), the electron sees a huge higher acceleration. Conductivity is proportional to the number of charge carriers and their mobility and the electrons are much more mobile - so make up the current flow in both positive and negitive streamers.
There is another picture in that link which is both interesting and "maybe" slightly humorous.. On page 12, there is a picture of an induced strke to a car "with a live rabbit inside". I didnt see in the paper if the rabbit lived.. but Im pretty sure its bunny brain probablly had to do a reboot shortly after the strike. (photo credit - page 12 of the link above)