How has and how does the lithosphere affect climate change? The climatic system can be divided into five main components: the atmosphere, the hydrosphere, the lithosphere, the cryosphere and the biosphere.

All these physical systems operate at different time and spatial scales. The lithosphere, that makes the uppermost, rigid layer of the earth, is formed by a few dozens of tectonic plates that move laterally while resting on the Earth's fluid mantle (plate tectonics). The collision between lithospheric plates builds mountains, and their separation forms ocean basins where sediment is accumulated, on timescales of tens to hundreds of millions of years. Hence, it is considered that its effect on climate change is not on the same timescale as the other components of the system and is not given as much attention.

Despite its low effect on the historical time-scales, undoubtedly, it poses a load on the system. Note that I am not interested on events that can in fact interact with the timescales of other climatic components. For example when land masses ocupied positions near the poles and the effect of the resulting increase in glaciation can be on the same time scale as other non-lithospheric physical phenomena. Nor am I interested in singular volcanic eruptions or activity of that sort. 

I am interested in how the processes such as continental drift, mountain growth, and erosion, affect climate evolution.
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.