Tomas, I use the templating very little, as most of my code is Ajax, but I originally did this with templates. I think you can do what you're suggesting, by building your menu in python and passing the text to the render function.
I think you prefer to avoid ajax and inject the menu into the render? So, assuming you already built your menu html into a string:
admin_menu = "some html"
class home:
def GET(self):
return render.home(admin_menu)
Then, in the home.html file in the templates directory, the first line would be:
$def with (content, menuhtml)
and somewhere on the page you'd have:
<div id="menu">$menuhtml</div>
I never did this with the 'base' template, but I'm sure it's similar.
Good luck!
S