Does lithium exist in near earth objects? Do we know if lithium exists in near Earth Object material and if so might it be economic to mine for future Earth-based transport?
 A: The answer is yes, lithium certainly exists in near-Earth objects. But whether it is financally viable to go and get it is a question outside the scope of Physics SE (but I doubt it is in the forseeable future),
I suppose you could define near-Earth objects (or at least a subset of those) being objects that actually impact the Earth. From that point of view, a lot of what we know about elemental abundances in the Solar System, particularly the "pristine" abundances before differentiation and other processes changed them in planetary bodies, are obtained from meteorites.
A well-cited reference for meteoritic abundances is Lodders (2003. Their Table 1 lists the abundances deduced from CI Chondrites (meteoritic abundances) and, for comparison, from analysis of the photsophere of the Sun.
Lithium is a particularly interesting element in this regard because it has a much higher abundance in meteorites, which essentially matches what we think is the current abundace of lithium in the interstellar medium. This abundance is expressed in terms of number of lithium atoms/nuclei as $A({\rm Li} = 3.28\pm 0.06$ on the usual logarithmic astronomical scale where hydrogen ($A({\rm H}$) would be 12.
The abundance of lithium in the solar photosphere is only $1.10\pm  0.10$ and this is because lithium is burned in nuclear reactions in the deep solar interior and the depleted material gradually mixed to the photosphere over billions of years.
