Question: I am not a physicist, but this question came to me and I need to answer it, and I think that you guys can help me. 

Is it possible to calculate the energy in a spark? For example in a lighter with an 'electric ignition'. 

If it is, how can I do that?

Answer: 
When you create a spark you generate a voltage, $V$, between the two electrodes and a current, $I$, flows between them. Both the voltage and the current vary with time, so we need to write them as functions of time: $V(t)$ and $I(t)$.

If we have a current $I$ flowing across a voltage $V$, then the power is given by:

$$ W = VI $$

Energy is power multiplied by time. So if we take a very short time $dt$ the energy in that time is:

$$ dE = VIdt $$

Now, in our system (the spark) both the voltage and current are functions of time, so to calculate the total energy we need to integrate $VIdt$:

$$ E = \int V(t) I(t) dt $$

And that's how we calculate the total energy in the spark.

But ...

Whether this answers your question or not I don't know, because I haven't actually calculated the energy. That's because I don't know how the voltage and current vary with time. How $V(t)$ and $I(t)$ vary with time will depend on the exact details of the spark. Obviously a gas lighter is going to be very different to a lightning bolt. There isn't an general rule to say how the voltageand current will vary with time so I can't provide a general answer. To actually calculate the energy in a spark would require detailed knowledge about the specific system you were considering.
One way is to connect the ignition to a high voltage (10kV) capacitor. Then the energy is:
$$E = \int VI d t = \frac{CV^2}{2},$$
where $C$ is its capacitance and $V$ its voltage, assuming that you connected it and did the measurements so that energy losses are negligible.