Obviously, the use of Liverpool and Stansted based aircraft on the Geneva is due to the fact that aircraft that would otherwise have no rotation are available to work the route. Geneva based aircraft are clearly not available. I would imagine that, during Summer, Easyjet currently have no aircraft available to work into LBA.
I think Easyjet expansion at LBA is possible, though limited. I certainly do not think an LBA base is a sensible idea as a number of routes Easyjet would be looking to serve with their based aircraft (Nice, Palma, Faro etc) are already well catered for. However, there are a number of Easyjet routes and bases that would be of significant interest to LBA imo.
Grenoble has been mentioned previously and that could certainly work as a Winter 'W' pattern from another UK airport. I would then be looking at tapping into the Madrid and Berlin bases, though any flights to these destinations would probably rely on additional aircraft being deployed to the aforementioned bases. Easyjet also have the benefit of the Madrid route having been tapped into from LBA previously, albeit by Jet2, which did ok without setting the world on fire. Easyjet could definitely take that route to the next level imo.
What is important in securing these extra flights (if at all possible) is how it is managed. There is no point going gung ho on a large expansion that is not an immediate success as Easyjet will just pull out again (DSA anyone?). A slower, more methodical approach would, more than likely, bring success.