I've wrangled a crazy way to have your cake and eat it too.

  do
    local state = 0
    function render()
      drawLine(0,5,0, 0,5,50*math.sin(state))
      state = state + math.pi * 0.03
    end
  end

To fiddle with the "state" variable from the outside:

  name,val = debug.getupvalue(render, 1)
  print(name) -- state
  print(val)  -- state's value

  debug.setupvalue(render, 1, 0) -- set state to 0

To find out how many upvalues are available:

  dt = debug.getinfo(render)
  print(dt.nups)

If you want to redefine render without disturbing state, you need to backup state and make a new closure with the new definition of render and the restored state:

  do
    local savedstate = {debug.getupvalue(render,1)}
    local state = savedstate[2]
    function render()
      local h = 5
      drawLine(0,h,0,50 * math.sin(state), h,0)
      state = state + math.pi * 0.06
    end
  end

I don't think its possible (or I don't know how) to redefine a function inside a closure. So just make a new closure and restore its state.