H1B amendment while H1B extension is in progress

[gunjanaol]

My H1B Visa valid till 08/31 and my employer has filed extension. Now I am getting into a new project(New client, new state).

I wanted to understand how it has to taken share since my H1B is already in extension. Do I need to resubmit my extension based on new project or just new LCA will be sufficient and usually how much time it takes to get the new LCA ? will I be able to start working for new project with my LCA ?

Thanks, Gunjan