You could apply the Technology Acceptance Model (TAM) proposed by Venkatesh to your research. The model describes behaviour towards adoption of technology (e-gov in this case) by measuring perceived ease of use, usefulness, etc.
A basic framework you do not want to ignore is Everet Roger's (1995) Diffusion of Innovation Theory. You may see how the theory is leveraged in e-government in my paper below.
Venkatesh's Technology Acceptance Model, Task Technology Fit, DeLone & McLean's IS Success Model (2002), Theory of Reasoned Action, Theory of Planned Behavior to name a few.
I believe that there is no single theory for the successful implementation of e-government. At the moment I'm developing a thesis for design an implementation model (successful) of eGob considering frameworks and IT governance standards and management theory programs, projects and plans. Any information that you need I can share with you, as you have
I am using the theory of critical success factor for examining the successful adoption of e-government. You can find my papers on this issue on the RG: https://www.researchgate.net/profile/Ewa_Ziemba
On determinants factors for e-government adoption for local government, you might find the following article of interest:
Significant socio-economic factors for local e-government development in Portugal (https://www.researchgate.net/publication/264822867_Significant_socio-economic_factors_for_local_e-government_development_in_Portugal)
Article Significant socio-economic factors for local e-government de...
I think this is a good read. Keep in mind the cultural differences always has a great impact on the any theory you may adapt. What works for one country may not guarantee the same result in another country or culture.
Factors Influencing Citizen Adoption of E-Government in Developing Countries: The Case of Jordan
Please see the following article which could provide you with some insight about this topic:
As-Saber, S. N., Hossain, M.K. and Srivastava, A. (2007). 'Technology, society and e-government: in search of an eclectic framework', Electronic Government: an International Journal, 4:156-178.
Alghamdi, I. A., Goodwin, R., & Rampersad, G. (2011). E-government readiness assessment for government organizations in developing countries. Computer and Information Science, 4(3), p3.