How has and how does the lithosphere affect climate change?
This is a huge and interesting topic. 
Certainly there are many ways the climate is affected by the lithosphere (and also what is going on in the asthenosphere). The lithosphere is naturally also affected by the climate. I find it difficult to distinguish the 'components' as matter and energy can flow from biosphere to lithosphere and from hydrosphere to atmosphere etc. Somehow it might be appealing to think about lithosphere as a slow 'component' but keep in mind that the atmospheric circulation have been much more stable than the locations of the continents. Deserts have been in the same latitudes, even as continents have been moving. 

A few areas of influence to consider: 


Location of landmasses affects ocean currents and climate e.g. closing of Isthmus of Panama.
Supercontinents certainly had a very different climate than what we experience today. 
Uplifts and orogenies can have local, regional and global effects. 
Carbonates in the lithosphere plays an important role the carbon cycle. See e.g. this.
Rate of vulcanism also follows tectonic conditions.