Energy Conservation Dilemma

From the perspective of the stationary observer, the light is dimmer. Why? Because the chemical reaction is happening more slowly, so the fire emits fewer photons per second. The flame burns for longer, but it emits less energy per second. Both observers will agree on the total energy emitted by the flame (once they have accounted for possible red-shift) and thus total energy is conserved.

Following on from @Jahan Claes' answer we can do some maths!

Say the man on the spaceship is using an ethanol burner. Ethanol has an enthalpy change of $1058 \text{ kJ}/\text{mol}$ but for simplicity let's say that it's equal to $1050$. If he burns $1$ mole of ethanol then it gives out approximately $1050 \text{ kJ}$. For the moving observer this is equal to $350\,000$ joules/min. For the stationary observer this will be equal to $210\,000$ joules/min.

Let's also say that the ethanol burner is giving out orange light, of a wavelength of $600 \text{ nm}$. Using the equation $$E = \frac{hc}{\lambda}$$ we can work out the energy of each photon to be roughly $3.315\times 10^{-19}$ (luckily for us the speed of light is the same for all observers). This means that the moving observer sees approximately $1.056\times 10^{24}$ photons every minute, whilst the stationary observer sees only approximately $6.335\times 10^{23}$ photons every minute.

From this we can see that $1.056(...)\times 10^{24}\times3 = 6.335(...)\times 10^{23}\times 5$ and everything works out just fine :)

You say the gas in the lighter is sufficient to be lit for 5 minutes, but whose 5 minutes? I guess you mean 5 mins as reckoned by the spaceship observer. In that case, for the observer at rest, the amount of gas in lighter is sufficient to be lit for $5\times (5/3)=8.3$ mins. So when spaceship observer lights the gas only for 3 mins and has 2 mins worth of gas left over, observer at rest sees that the gas has been lit for 5 mins and 3.3 mins worth of gas is left over. There is no contradiction or violation of any law.

P.S. If you say that the amount of gas in the lighter can burn for 5 mins as per observer at rest, then from spaceship observer's point of view the lighter contains only 3 mins worth of gas. Then if he lights it for 3 mins there cannot be any gas left inside the lighter.