You'll be having earthquakes soon. Take it there are no gas seems so fracking as well is out?
The most likely method for extraction, think thermal springs. Drill two bore holes, hot water comes up (rich in lithium), extract the lithium and shove the water back down the other hole. This is the greenest method and it has potential for energy supply as well.
Alternatively it's breaking down the granite to extract the lithium deposits. In most areas the granite is only several feet below the surface so any mining would be open cast and would depend on where the richest sources are.
Cornish Lithium Ltd | Lithium exploration within Cornwall, UK
Where I live china clay was extensively mined, extracted from the granite, all open cast. It's still mined today but only a fraction of what was once mined. If you have a look at St Austell on Google Earth you'll see the extent of the mining and the proximity of the granite to the surface. No need to crawl down flooded holes.
