You can use reflection and construct your call like this:
Type MyType = Type.GetType(FromSomewhereElse);
var typeOfContext = context.GetType();
var method = typeOfContext.GetMethod("GetList");
var genericMethod = method.MakeGenericMethod(MyType);
genericMethod.Invoke(context, null);
Note that calling methods with reflection will add a huge performance penalty, try to redesign your solution if possible.