What's wrong with this latching relay circuit?
The error is in wiring the lamp in series with the relay coil thereby reducing the current through both. Added to that would be the clipping effect of the LED.
That circuit would only function if it used a 12 V AC lamp and a 12 V AC relay, both having the same current rating.
Here's how the AC version ought to be. An RC snubber is to be connected across the relay coil to suppress voltage transients during turn-off.
Two LEDs in parallel protect themselves from the reverse voltage of the AC supply.

Here's the DC version. A freewheeling diode is to be connected across the relay coil.