The main problem is that the lower LED does not have a resistor in series with it.
When the output goes high, there is nothing to limit the current to the LED.
What eventually limits the current will be a mix of various distributed resistances that you normally don't consider. These will include:
- Internal resistance of the battery
- resistance in the wiring
- resistance in internal to the 555
- V vs I curve of the LED.
Whichever one dominates will probably get the hottest. In your case it is the internal resistances in the 555. This is probably dominated by the voltage drop across the transistor switching current to the LED, although there will be other things contributing to it. If you measure your battery voltage you will also probably note that it drops significantly.
As an aside, if you powered this circuit using a 12V car battery, I expect you would pretty much immediately see smoke coming from the 555 and really bad things happening to the LED. It would be an interesting race to see which managed to fail open circuit first. You might even get one (or possibly both) to go *BANG*.
Yeah, having series resistors is a really good idea.